Linearity

Problem 2301

Find the equation in slope-intercept form for a line with slope -5 and y-intercept 3.

See Solution

Problem 2302

Find the intersection point $(x, y)$ of the two linear equations given their points:
1st: $(-2, 15), (0, 11), (2, 8), (4, 5)$ 2nd: $(-2, 4), (0, 6.5), (2, 8), (4, 9.5)$ .

See Solution

Problem 2303

Solve the system of equations: $x+y=7$ and $x-2y=4$ .

See Solution

Problem 2304

Complete the table for the function where the output is $4n + 1$ . Find the output for $n = 5$ and beyond.

See Solution

Problem 2305

Jay has 10 baseball cards and buys 1 each month. Model the total cards after $n$ months: $C(n) = 10 + n$ .

See Solution

Problem 2306

Find three integers that differ by 3, where 5 times the largest equals 3 times the smallest plus 5 times the middle.

See Solution

Problem 2307

Fritz's drive takes 48 min, train 40 min. Train is 6 mph faster. Find distance $d$ he travels to work. Simplify $d$ .

See Solution

Problem 2308

Jane took 10 min upstream and 5 min downstream. If the current is $6 \mathrm{~km}$ /hr, find her boat speed in still water.

See Solution

Problem 2309

How many quarts of pure antifreeze are needed to change 5 quarts of a $30\%$ solution to a $40\%$ solution?

See Solution

Problem 2310

Solve the equation: $-(1-5 x)+8=-17+2 x$ .

See Solution

Problem 2311

Solve the equation: $2(-7a + 6) = -16 - 7a$ .

See Solution

Problem 2312

Margaret drove to an appointment at $90 \mathrm{mph}$ and returned at $80 \mathrm{mph}$ , taking $\frac{1}{8} \mathrm{hr}$ longer. Find the distance.

See Solution

Problem 2313

Simplify the expression: $9n - 8 + 3(2n - 11)$ .

See Solution

Problem 2314

How many quarts of pure antifreeze are needed to change 5 quarts of a $30\%$ solution to a $40\%$ solution?

See Solution

Problem 2315

Jane took 20 min to go upstream and 10 min to return. If the current is 8 km/hr, find her boat speed in still water in km/hr.

See Solution

Problem 2316

A mother earned \$6250. She set aside 20% for a home, invested the rest at 4% and 7%, earning \$300 interest. Find the CD investment.

See Solution

Problem 2317

Evaluate the expression for $c=7$ and $y=-4$ : $-c + 8y$ .

See Solution

Problem 2318

Evaluate $-4x + c$ for $c = -6$ and $x = 3$ .

See Solution

Problem 2319

Solve the equation: $5(6 x-2)+9=30 x-1$ .

See Solution

Problem 2320

Solve the equation: $4(3 x-8)-1=12 x-36$ .

See Solution

Problem 2321

Solve for $x$ : $7(x+4)+2=-4(x-11)-8$

See Solution

Problem 2322

Розв'яжи рівняння: $x-3765=654$ .

See Solution

Problem 2323

Знайди перше число, якщо друге число на 15 менше від першого і дорівнює 93: $x - 15 = 93$ .

See Solution

Problem 2324

Determine the line equation through the point $(-3,1)$ with a slope of $-2$ .

See Solution

Problem 2325

Solve for $x$ : $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ .

See Solution

Problem 2326

Find the equation of the line through $(-5,-5)$ , parallel to $y=\frac{2}{5}x+4$ .

See Solution

Problem 2327

Solve the equation: $\frac{1}{4}(x-3)=\frac{1}{2}$ .

See Solution

Problem 2328

Solve for $x$ in the equation $\frac{x}{8}+15=17$ .

See Solution

Problem 2329

Find the line equation in point-slope form through points $(-5,1)$ and $(3,1)$ .

See Solution

Problem 2330

Solve the equation: $\frac{x-8}{3}=\frac{2}{3}$ .

See Solution

Problem 2331

Find the unit rate for the whale's speed, and the vertical and horizontal changes between points $(2.5,1)$ and $(5,2)$ .

See Solution

Problem 2332

Scott uses 43-cent and 6-cent stamps to make \$1.77. How many of each stamp did he use?

See Solution

Problem 2333

Find a number $x$ such that $12x + 4 = 4 \times 10$ .

See Solution

Problem 2334

In a field with 30 heads and 82 feet, how many pigs and chickens are there? Let pigs be $p$ and chickens be $c$ . Solve:
1. $p + c = 30$
2. $4p + 2c = 82$

See Solution

Problem 2335

Identify equivalent equations to $54-z=70$ using properties of equality from the options provided.

See Solution

Problem 2336

Select all equations equivalent to $9=10 s$ : $6=10 s-2$ , $7=10 s-2$ , $4=10 s-5$ , $8=10 s-3$ .

See Solution

Problem 2337

Select the equivalent equations to $f+g=5$ using properties of equality: $f+g+4=7$ , $11+f+g=18$ , $8+f+g=14$ , $11+f+g=16$ .

See Solution

Problem 2338

Choose all equivalent equations to: $7=7-y$ . Options are: $3=7-y-4$ , $7=7-y-2$ , $4=7-y-3$ , $2=7-y-5$ .

See Solution

Problem 2339

Lösen Sie die folgenden linearen Gleichungen über R:
1. a) $3x + 5 = 23$ b) $8x - 12 = 28$ c) $10y + 23 = 3$ d) $11 - 5z = 26$ e) $4z - 9 = -2$ f) $12y + 15 = 19$ g) $80 - 12t = 38$ h) $16 = 7z + 30$
2. a) $7x + 3 = 5x + 12$ b) $6z + 8 = 11z - 7$ c) $9y + 4 = 3y - 10$ d) $100 - 7x = 13x$ e) $0.9x + 5 = 1.2x - 3.4$ f) $4.2t - 7 = 11 - 3.3t$ g) $0.7y + 2.8 = 0.55y - 1.7$ h) $0.5 - 1.7z = 0.74 + 2.3z$
3. a) $\frac{2x}{3} + 2 = 10$ b) $\frac{3x}{5} - 5 = 7$ c) $\frac{x}{2} + \frac{x}{3} = 25$ d) $\frac{y}{3} + \frac{y}{4} + 15 = y$ e) $\frac{z}{3} - \frac{z}{5} = 1$ f) $\frac{u}{5} + 2 = \frac{u}{3} - 4$ g) $\frac{3z}{4} = \frac{2z}{3} - 5$ h) $\frac{5y}{8} = \frac{2y}{5} + 3$
4. a) $3(x + 7) = 4(2x - 1)$ b) $4(5x - 3) + 6 = 10$ c) $8(y + 10) - 30 = 5y$ d) $9(y - 5) = 4y - 10$ e) $3(6v + 4) = 9(2v - 3)$ f) $8(3 + 2z) - 3z = 5z - 8$ g) $5(y - 0.2) = 1.6(3y + 0.5)$ h) $4(9w - 11) - 12(3w - 4) = 4$
5. a) $\frac{3y + 5}{2} = \frac{2y}{3}$ b) $\frac{x + 5}{3} = \frac{3x}{4}$ c) $\frac{2x - 5}{2} = \frac{4x - 9}{5}$ d) $\frac{4x + 30}{6} = \frac{9 - x}{4}$ e) $\frac{2z + 7}{5} = \frac{9 - 3z}{6}$ f) $\frac{3y + 4}{4} = \frac{4y - 6}{5}$ g) $\frac{4z + 1}{6} = \frac{z - 3}{2} + \frac{2}{3}$ h) $\frac{y + 2}{3} + \frac{y - 1}{15} = \frac{2y + 3}{5}$

See Solution

Problem 2340

Select all equations equivalent to $f+g=5$ using properties of equality: $f+g+4=7$ , $11+f+g=18$ , $8+f+g=14$ , $11+f+g=16$ .

See Solution

Problem 2341

Select equations equivalent to $12=5 j$ using properties of equality: $19=7+5 j$ , $16=5 j+4$ , $15=5 j+3$ , $17=5+5 j$ .

See Solution

Problem 2342

Find the slope of the line through points (-1,-2) and (3,0): $m=\frac{0-(-2)}{3-(-1)}=[?]$ . Options: A. $-2/4$ , B. $1/2$ , C. 0, D. $-2/2$ .

See Solution

Problem 2343

What are the inputs to the slope formula for points (-1,-2) and (3,0)?
$m=\frac{0--2}{[?]-(-1)}$
A. 0 B. -2 C. -1 D. 3

See Solution

Problem 2344

Find the equation in point-slope form of a line with slope $m=-3$ through the point $(8,2)$ .

See Solution

Problem 2345

Find the point-slope form of the line with slope $m=-3$ through the point $(5,3)$ . $y-[?]=\square(x-\square)$

See Solution

Problem 2346

Find the equation in point-slope form of a line with slope $m=-5$ through the point $(4,-2)$ .

See Solution

Problem 2347

Find the equation of the line in point-slope form using the point $(-5,1)$ with slope $m=2$ . $y-1=2(x-[?])$

See Solution

Problem 2348

Find the slope of the line through points $(12,3)$ and $(6,1)$ . Slope = $\frac{[}{[]}$

See Solution

Problem 2349

Find the slope of the line through $(12,3)$ and $(6,1)$ . Then use the slope-intercept formula to find $b$ .

See Solution

Problem 2350

Find the slope of the line through points $(12,3)$ and $(6,1)$ . Then complete the slope-intercept formula: $3=\frac{1}{3}[?]+b$ .

See Solution

Problem 2351

Find the slope of the line through $(-9,-2)$ and $(5,1)$ , then use it in the slope-intercept formula.

See Solution

Problem 2352

Solve for $x$ in the equation: $\frac{1}{3} x + 3 = \frac{14}{3}$ .

See Solution

Problem 2353

Solve for $x$ : $\frac{1}{3} x + 3 = \frac{14}{3}$ .

See Solution

Problem 2354

Find the slope of the line through points $(-3,-3)$ and $(-5,10)$ . Slope = $[\frac{[]}{[]}]$

See Solution

Problem 2355

Find two consecutive integers whose sum is 109.

See Solution

Problem 2356

Find three consecutive even integers whose sum is 24.

See Solution

Problem 2357

Find three consecutive integers whose sum is 81.

See Solution

Problem 2358

Find three consecutive odd integers that add up to 45.

See Solution

Problem 2359

Rewrite the equation $9 x + 3 y = 12$ in function notation with $x$ as the independent variable.

See Solution

Problem 2360

Write the function $9x + 3y = 12$ in function notation as $f(x)$ .

See Solution

Problem 2361

The garden table and bench cost \$600 together. The table costs three times the bench. Find the bench's cost.

See Solution

Problem 2362

Rewrite the equation $y - 6x - 9 = 0$ in function notation with $x$ as the independent variable.

See Solution

Problem 2363

Solve $2+\frac{1}{6} x=-4$ . Find the value of $x$ .

See Solution

Problem 2364

Solve the equation $-6 x - \frac{3}{7} = \frac{4}{7}$ . Find $x =$ .

See Solution

Problem 2365

Solve $-\frac{1}{2} x - 7 = 18$ for $x$ . What is the value of $x$ ?

See Solution

Problem 2366

Solve $-9=\frac{2}{7} x+5$ for $x$ . What is the value of $x$ ?

See Solution

Problem 2367

Find $BC$ given $AB=9$ , $AC=5x-1$ , and $BC=2x+2$ .

See Solution

Problem 2368

Which expression equals $3m + m - 6m$ ? Options: $1 - 3m$ , $m - 3$ , $-8m$ , $-2m$ .

See Solution

Problem 2369

Solve the equation: $6x - 8 = 10x + 16$ . Find the solution set.

See Solution

Problem 2370

Solve for $y$ in the equation: $3y - 9x = -6$ .

See Solution

Problem 2371

Solve for $y$ : $y + 1 = \frac{1}{2}(10x - 12)$

See Solution

Problem 2372

Solve for $y$ in the equation: $3x - y = 9$ .

See Solution

Problem 2373

Solve for $y$ : $y - 20 = -3(x - 6)$

See Solution

Problem 2374

Find $y$ in the equation: $3x - y = 9$ .

See Solution

Problem 2375

Find the equation of a line through $(-4,4)$ that is perpendicular to $y=\frac{1}{2}x+2$ .

See Solution

Problem 2376

Find the slope of the line through points $(-3,8)$ and $(4,7)$ . Show your calculations.

See Solution

Problem 2377

Find the slope of the line through points $(-3,8)$ and $(4,7)$ . Show your work.

See Solution

Problem 2378

Find the slope between points (0,0) and (1,30) on the line. Can you find another pair of points with a different slope?

See Solution

Problem 2379

A marine biologist studies a dolphin's speed. It swims 55 meters in 5 seconds. Graph the distance over time. How far in 1 second?

See Solution

Problem 2380

Find the constant of proportionality for the values: (-4, -24), (0, 0), (7, 42), (11, 66), (15, 90).

See Solution

Problem 2381

Find the cups of sugar for 1 cup of flour, given the ratio: 2 cups sugar to 5 cups flour.

See Solution

Problem 2382

Намери стойността на $y$ , ако $x: y=2: 3$ , $x: z=4: 3$ и $2x - y + z = 15$ .

See Solution

Problem 2383

А) 20. Ако $x: y=2: 3$ , $x: z=4: 3$ и $2x-y+z=15$ , намерете стойността на $y$ .

See Solution

Problem 2384

A merchant mixes $x$ kg of tea at \ $72/kg with$ y $kg at \$97/kg for a mixture cost of \$82/kg. Find$ x:y$ and profit from 15 kg of tea P sold at \$120/kg.

See Solution

Problem 2385

Solve the equation $4x + 2 = 2(5 - 2x)$ .

See Solution

Problem 2386

En un congreso, la relación inicial es 8 varones por 5 mujeres. Tras retirar 25 mujeres, hay 5 mujeres por 12 varones. ¿Cuántas personas había inicialmente?

See Solution

Problem 2387

Solve for $x$ in the equation $7x + 4 = 39$ . What is the value of $x$ ? Options: 4, 5, 35, 43.

See Solution

Problem 2388

If the final price is \$3 after halving the new price, what was the original price before the \$2 increase?

See Solution

Problem 2389

Solve the equation: $\frac{1}{4}\left(x+\frac{1}{2}\right)=\frac{7}{8}$ .

See Solution

Problem 2390

Solve for $x$ in the equation $\frac{1}{2} x - 2 = \frac{1}{5}$ .

See Solution

Problem 2391

Solve for $x$ : $\frac{x-5}{5}=\frac{3}{5}$ .

See Solution

Problem 2392

Colleen uses blue yarn $b$ and red yarn $r$ . What equation shows their proportional relationship? Options: (A) $b=\frac{2}{5} r$ , (B) $r=\frac{2}{5} b$ , (C) $b=\frac{2}{7} r$ , (D) $r=\frac{2}{7} b$ .

See Solution

Problem 2393

Concert tickets cost \$35 and \$55. If 95 tickets sold for \$4325, find how many of each type were sold.

See Solution

Problem 2394

Find the inverse of the function $f(x)=2x+1$ .

See Solution

Problem 2395

Find the inverse of the function $f(x)=\frac{1}{9} x+2$ .

See Solution

Problem 2396

Find $f(8)$ for the function $f(x)=6x-4$ .

See Solution

Problem 2397

Dan completes a painting every 3 weeks. John shovels snow for 5 houses in 2 hours. How long for 13 houses? Baxter boys prep 25 papers in 3 min. Time for 131 papers?

See Solution

Problem 2398

In 2008, 345k girls played soccer and 458k in track. Rate: soccer +8k/yr, track +3k/yr.
a. Write equations for $y$ in terms of $x$ .
b. Show $(22.5, 525)$ is an approximate solution.

See Solution

Problem 2399

A train station parking garage has two plans: Plan A: R55 + R21 per day. Plan B costs given for days parked. Find the system of equations for total cost $C$ and days $n$ .

See Solution

Problem 2400

Graph the line given by the equation $y + 2 = 2(x + 1)$ . Select points on the graph and submit.

See Solution

1 ...21 22 23 24 25 26 27 ...77

Linearity

Problem 2301

Find the equation in slope-intercept form for a line with slope -5 and y-intercept 3.

Problem 2302

Find the intersection point (x,y)(x, y)(x,y) of the two linear equations given their points: 1st: (−2,15),(0,11),(2,8),(4,5)(-2, 15), (0, 11), (2, 8), (4, 5)(−2,15),(0,11),(2,8),(4,5) 2nd: (−2,4),(0,6.5),(2,8),(4,9.5)(-2, 4), (0, 6.5), (2, 8), (4, 9.5)(−2,4),(0,6.5),(2,8),(4,9.5).

Problem 2303

Solve the system of equations: x+y=7x+y=7x+y=7 and x−2y=4x-2y=4x−2y=4.

Problem 2304

Complete the table for the function where the output is 4n+14n + 14n+1. Find the output for n=5n = 5n=5 and beyond.

Problem 2305

Jay has 10 baseball cards and buys 1 each month. Model the total cards after nnn months: C(n)=10+nC(n) = 10 + nC(n)=10+n.

Problem 2306

Find three integers that differ by 3, where 5 times the largest equals 3 times the smallest plus 5 times the middle.

Problem 2307

Fritz's drive takes 48 min, train 40 min. Train is 6 mph faster. Find distance ddd he travels to work. Simplify ddd.

Problem 2308

Jane took 10 min upstream and 5 min downstream. If the current is 6 km6 \mathrm{~km}6 km/hr, find her boat speed in still water.

Problem 2309

How many quarts of pure antifreeze are needed to change 5 quarts of a 30%30\%30% solution to a 40%40\%40% solution?

Problem 2310

Solve the equation: −(1−5x)+8=−17+2x-(1-5 x)+8=-17+2 x−(1−5x)+8=−17+2x.

Problem 2311

Solve the equation: 2(−7a+6)=−16−7a2(-7a + 6) = -16 - 7a2(−7a+6)=−16−7a.

Problem 2312

Margaret drove to an appointment at 90mph90 \mathrm{mph}90mph and returned at 80mph80 \mathrm{mph}80mph, taking 18hr\frac{1}{8} \mathrm{hr}81​hr longer. Find the distance.

Problem 2313

Simplify the expression: 9n−8+3(2n−11)9n - 8 + 3(2n - 11)9n−8+3(2n−11).

Problem 2314

How many quarts of pure antifreeze are needed to change 5 quarts of a 30%30\%30% solution to a 40%40\%40% solution?

Problem 2315

Jane took 20 min to go upstream and 10 min to return. If the current is 8 km/hr, find her boat speed in still water in km/hr.

Problem 2316

A mother earned \$6250. She set aside 20% for a home, invested the rest at 4% and 7%, earning \$300 interest. Find the CD investment.

Problem 2317

Evaluate the expression for c=7c=7c=7 and y=−4y=-4y=−4: −c+8y-c + 8y−c+8y.

Problem 2318

Evaluate −4x+c-4x + c−4x+c for c=−6c = -6c=−6 and x=3x = 3x=3.

Problem 2319

Solve the equation: 5(6x−2)+9=30x−15(6 x-2)+9=30 x-15(6x−2)+9=30x−1.

Problem 2320

Solve the equation: 4(3x−8)−1=12x−364(3 x-8)-1=12 x-364(3x−8)−1=12x−36.

Problem 2321

Solve for xxx: 7(x+4)+2=−4(x−11)−87(x+4)+2=-4(x-11)-87(x+4)+2=−4(x−11)−8

Problem 2322

Розв'яжи рівняння: x−3765=654x-3765=654x−3765=654.

Problem 2323

Знайди перше число, якщо друге число на 15 менше від першого і дорівнює 93: x−15=93x - 15 = 93x−15=93.

Problem 2324

Determine the line equation through the point (−3,1)(-3,1)(−3,1) with a slope of −2-2−2.

Problem 2325

Solve for xxx: 13x+14x−2=x−7\frac{1}{3} x+\frac{1}{4} x-2=x-731​x+41​x−2=x−7.

Problem 2326

Find the equation of the line through (−5,−5)(-5,-5)(−5,−5), parallel to y=25x+4y=\frac{2}{5}x+4y=52​x+4.

Problem 2327

Solve the equation: 14(x−3)=12\frac{1}{4}(x-3)=\frac{1}{2}41​(x−3)=21​.

Problem 2328

Solve for xxx in the equation x8+15=17\frac{x}{8}+15=178x​+15=17.

Problem 2329

Find the line equation in point-slope form through points (−5,1)(-5,1)(−5,1) and (3,1)(3,1)(3,1).

Problem 2330

Solve the equation: x−83=23\frac{x-8}{3}=\frac{2}{3}3x−8​=32​.

Problem 2331

Find the unit rate for the whale's speed, and the vertical and horizontal changes between points (2.5,1)(2.5,1)(2.5,1) and (5,2)(5,2)(5,2).

Problem 2332

Scott uses 43-cent and 6-cent stamps to make \$1.77. How many of each stamp did he use?

Problem 2333

Find a number xxx such that 12x+4=4×1012x + 4 = 4 \times 1012x+4=4×10.

Problem 2334

In a field with 30 heads and 82 feet, how many pigs and chickens are there? Let pigs be ppp and chickens be ccc. Solve: 1. p+c=30p + c = 30p+c=30 2. 4p+2c=824p + 2c = 824p+2c=82

Problem 2335

Identify equivalent equations to 54−z=7054-z=7054−z=70 using properties of equality from the options provided.

Problem 2336

Select all equations equivalent to 9=10s9=10 s9=10s: 6=10s−26=10 s-26=10s−2, 7=10s−27=10 s-27=10s−2, 4=10s−54=10 s-54=10s−5, 8=10s−38=10 s-38=10s−3.

Problem 2337

Select the equivalent equations to f+g=5f+g=5f+g=5 using properties of equality: f+g+4=7f+g+4=7f+g+4=7, 11+f+g=1811+f+g=1811+f+g=18, 8+f+g=148+f+g=148+f+g=14, 11+f+g=1611+f+g=1611+f+g=16.

Problem 2338

Choose all equivalent equations to: 7=7−y7=7-y7=7−y. Options are: 3=7−y−43=7-y-43=7−y−4, 7=7−y−27=7-y-27=7−y−2, 4=7−y−34=7-y-34=7−y−3, 2=7−y−52=7-y-52=7−y−5.

Problem 2339

Problem 2340

Select all equations equivalent to f+g=5f+g=5f+g=5 using properties of equality: f+g+4=7f+g+4=7f+g+4=7, 11+f+g=1811+f+g=1811+f+g=18, 8+f+g=148+f+g=148+f+g=14, 11+f+g=1611+f+g=1611+f+g=16.

Find the intersection point $(x, y)$ of the two linear equations given their points:
1st: $(-2, 15), (0, 11), (2, 8), (4, 5)$ 2nd: $(-2, 4), (0, 6.5), (2, 8), (4, 9.5)$ .

Solve the system of equations: $x+y=7$ and $x-2y=4$ .

Complete the table for the function where the output is $4n + 1$ . Find the output for $n = 5$ and beyond.

Jay has 10 baseball cards and buys 1 each month. Model the total cards after $n$ months: $C(n) = 10 + n$ .

Fritz's drive takes 48 min, train 40 min. Train is 6 mph faster. Find distance $d$ he travels to work. Simplify $d$ .

Jane took 10 min upstream and 5 min downstream. If the current is $6 \mathrm{~km}$ /hr, find her boat speed in still water.

How many quarts of pure antifreeze are needed to change 5 quarts of a $30\%$ solution to a $40\%$ solution?

Solve the equation: $-(1-5 x)+8=-17+2 x$ .

Solve the equation: $2(-7a + 6) = -16 - 7a$ .

Margaret drove to an appointment at $90 \mathrm{mph}$ and returned at $80 \mathrm{mph}$ , taking $\frac{1}{8} \mathrm{hr}$ longer. Find the distance.

Simplify the expression: $9n - 8 + 3(2n - 11)$ .

How many quarts of pure antifreeze are needed to change 5 quarts of a $30\%$ solution to a $40\%$ solution?

Evaluate the expression for $c=7$ and $y=-4$ : $-c + 8y$ .

Evaluate $-4x + c$ for $c = -6$ and $x = 3$ .

Solve the equation: $5(6 x-2)+9=30 x-1$ .

Solve the equation: $4(3 x-8)-1=12 x-36$ .

Solve for $x$ : $7(x+4)+2=-4(x-11)-8$

Розв'яжи рівняння: $x-3765=654$ .

Знайди перше число, якщо друге число на 15 менше від першого і дорівнює 93: $x - 15 = 93$ .

Determine the line equation through the point $(-3,1)$ with a slope of $-2$ .

Solve for $x$ : $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ .

Find the equation of the line through $(-5,-5)$ , parallel to $y=\frac{2}{5}x+4$ .

Solve the equation: $\frac{1}{4}(x-3)=\frac{1}{2}$ .

Solve for $x$ in the equation $\frac{x}{8}+15=17$ .

Find the line equation in point-slope form through points $(-5,1)$ and $(3,1)$ .

Solve the equation: $\frac{x-8}{3}=\frac{2}{3}$ .

Find the unit rate for the whale's speed, and the vertical and horizontal changes between points $(2.5,1)$ and $(5,2)$ .

Find a number $x$ such that $12x + 4 = 4 \times 10$ .

In a field with 30 heads and 82 feet, how many pigs and chickens are there? Let pigs be $p$ and chickens be $c$ . Solve:
1. $p + c = 30$
2. $4p + 2c = 82$

Identify equivalent equations to $54-z=70$ using properties of equality from the options provided.

Select all equations equivalent to $9=10 s$ : $6=10 s-2$ , $7=10 s-2$ , $4=10 s-5$ , $8=10 s-3$ .

Select the equivalent equations to $f+g=5$ using properties of equality: $f+g+4=7$ , $11+f+g=18$ , $8+f+g=14$ , $11+f+g=16$ .

Choose all equivalent equations to: $7=7-y$ . Options are: $3=7-y-4$ , $7=7-y-2$ , $4=7-y-3$ , $2=7-y-5$ .

Select all equations equivalent to $f+g=5$ using properties of equality: $f+g+4=7$ , $11+f+g=18$ , $8+f+g=14$ , $11+f+g=16$ .

Select equations equivalent to $12=5 j$ using properties of equality: $19=7+5 j$ , $16=5 j+4$ , $15=5 j+3$ , $17=5+5 j$ .

Find the slope of the line through points (-1,-2) and (3,0): $m=\frac{0-(-2)}{3-(-1)}=[?]$ . Options: A. $-2/4$ , B. $1/2$ , C. 0, D. $-2/2$ .

What are the inputs to the slope formula for points (-1,-2) and (3,0)?
$m=\frac{0--2}{[?]-(-1)}$
A. 0 B. -2 C. -1 D. 3

Find the equation in point-slope form of a line with slope $m=-3$ through the point $(8,2)$ .

Find the point-slope form of the line with slope $m=-3$ through the point $(5,3)$ . $y-[?]=\square(x-\square)$

Find the equation in point-slope form of a line with slope $m=-5$ through the point $(4,-2)$ .

Find the equation of the line in point-slope form using the point $(-5,1)$ with slope $m=2$ . $y-1=2(x-[?])$

Find the slope of the line through points $(12,3)$ and $(6,1)$ . Slope = $\frac{[}{[]}$

Find the slope of the line through $(12,3)$ and $(6,1)$ . Then use the slope-intercept formula to find $b$ .

Find the slope of the line through points $(12,3)$ and $(6,1)$ . Then complete the slope-intercept formula: $3=\frac{1}{3}[?]+b$ .

Find the slope of the line through $(-9,-2)$ and $(5,1)$ , then use it in the slope-intercept formula.

Solve for $x$ in the equation: $\frac{1}{3} x + 3 = \frac{14}{3}$ .

Solve for $x$ : $\frac{1}{3} x + 3 = \frac{14}{3}$ .

Find the slope of the line through points $(-3,-3)$ and $(-5,10)$ . Slope = $[\frac{[]}{[]}]$

Rewrite the equation $9 x + 3 y = 12$ in function notation with $x$ as the independent variable.

Write the function $9x + 3y = 12$ in function notation as $f(x)$ .

Rewrite the equation $y - 6x - 9 = 0$ in function notation with $x$ as the independent variable.

Solve $2+\frac{1}{6} x=-4$ . Find the value of $x$ .

Solve the equation $-6 x - \frac{3}{7} = \frac{4}{7}$ . Find $x =$ .

Solve $-\frac{1}{2} x - 7 = 18$ for $x$ . What is the value of $x$ ?

Solve $-9=\frac{2}{7} x+5$ for $x$ . What is the value of $x$ ?

Find $BC$ given $AB=9$ , $AC=5x-1$ , and $BC=2x+2$ .

Which expression equals $3m + m - 6m$ ? Options: $1 - 3m$ , $m - 3$ , $-8m$ , $-2m$ .

Solve the equation: $6x - 8 = 10x + 16$ . Find the solution set.

Solve for $y$ in the equation: $3y - 9x = -6$ .

Solve for $y$ : $y + 1 = \frac{1}{2}(10x - 12)$

Solve for $y$ in the equation: $3x - y = 9$ .

Solve for $y$ : $y - 20 = -3(x - 6)$

Find $y$ in the equation: $3x - y = 9$ .