Question12. Find another point on a line with slope $-\frac{2}{3}$ and point $A$ at $(-1,-5)$ .
13. A ladder leans against a wall. Its base is $1.5 \mathrm{m}$ from the wall, and its top touches the wall $4 \mathrm{~m}$ above the ground. Find the ladder's slope.

Studdy Solution

STEP 1

For problem 12:
Assumptions
1. The coordinates of point A are $(-1, -5)$ .
2. The slope of the line is $-\frac{2}{3}$ .
3. We need to find the coordinates of another point B on the line.

STEP 2

The slope of a line is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line.
$Slope = \frac{\Delta y}{\Delta x}$

STEP 3

Using the given slope and the coordinates of point A, we can find the coordinates of another point B by choosing a value for $\Delta x$ and calculating the corresponding $\Delta y$ .
$-\frac{2}{3} = \frac{\Delta y}{\Delta x}$

STEP 4

Choose a convenient value for $\Delta x$ . Let's choose $\Delta x = 3$ since it will cancel out the denominator of the slope.
$\Delta x = 3$

STEP 5

Calculate the corresponding $\Delta y$ using the slope.
$\Delta y = Slope \times \Delta x$
$\Delta y = -\frac{2}{3} \times 3$

STEP 6

Simplify the calculation for $\Delta y$ .
$\Delta y = -\frac{2}{3} \times 3 = -2$

STEP 7

Now we can find the coordinates of point B by adding $\Delta x$ and $\Delta y$ to the coordinates of point A.
$B_x = A_x + \Delta x$
$B_y = A_y + \Delta y$

STEP 8

Calculate the x-coordinate for point B.
$B_x = -1 + 3 = 2$

STEP 9

Calculate the y-coordinate for point B.
$B_y = -5 - 2 = -7$

STEP 10

Combine the x and y coordinates to get the coordinates of point B.
$Coordinates\, of\, point\, B = (2, -7)$
Another point on the line is $(2, -7)$ .

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Question12. Find another point on a line with slope $-\frac{2}{3}$ and point $A$ at $(-1,-5)$ .
13. A ladder leans against a wall. Its base is $1.5 \mathrm{m}$ from the wall, and its top touches the wall $4 \mathrm{~m}$ above the ground. Find the ladder's slope.

Studdy Solution

STEP 1

For problem 12:
Assumptions
1. The coordinates of point A are $(-1, -5)$ .
2. The slope of the line is $-\frac{2}{3}$ .
3. We need to find the coordinates of another point B on the line.

STEP 2

The slope of a line is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line.
$Slope = \frac{\Delta y}{\Delta x}$

STEP 3

Using the given slope and the coordinates of point A, we can find the coordinates of another point B by choosing a value for $\Delta x$ and calculating the corresponding $\Delta y$ .
$-\frac{2}{3} = \frac{\Delta y}{\Delta x}$

STEP 4

Choose a convenient value for $\Delta x$ . Let's choose $\Delta x = 3$ since it will cancel out the denominator of the slope.
$\Delta x = 3$

STEP 5

Calculate the corresponding $\Delta y$ using the slope.
$\Delta y = Slope \times \Delta x$
$\Delta y = -\frac{2}{3} \times 3$

STEP 6

Simplify the calculation for $\Delta y$ .
$\Delta y = -\frac{2}{3} \times 3 = -2$

STEP 7

Now we can find the coordinates of point B by adding $\Delta x$ and $\Delta y$ to the coordinates of point A.
$B_x = A_x + \Delta x$
$B_y = A_y + \Delta y$

STEP 8

Calculate the x-coordinate for point B.
$B_x = -1 + 3 = 2$

STEP 9

Calculate the y-coordinate for point B.
$B_y = -5 - 2 = -7$

STEP 10

Combine the x and y coordinates to get the coordinates of point B.
$Coordinates\, of\, point\, B = (2, -7)$
Another point on the line is $(2, -7)$ .

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Studdy Solution

STEP 1

For problem 12:Assumptions1. The coordinates of point A are (−1,−5)(-1, -5)(−1,−5).2. The slope of the line is −23-\frac{2}{3}−32​.3. We need to find the coordinates of another point B on the line.

STEP 2

The slope of a line is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line.Slope=ΔyΔxSlope = \frac{\Delta y}{\Delta x}Slope=ΔxΔy​

STEP 3

Using the given slope and the coordinates of point A, we can find the coordinates of another point B by choosing a value for Δx\Delta xΔx and calculating the corresponding Δy\Delta yΔy.−23=ΔyΔx-\frac{2}{3} = \frac{\Delta y}{\Delta x}−32​=ΔxΔy​

STEP 4

Choose a convenient value for Δx\Delta xΔx. Let's choose Δx=3\Delta x = 3Δx=3 since it will cancel out the denominator of the slope.Δx=3\Delta x = 3Δx=3

STEP 5

Calculate the corresponding Δy\Delta yΔy using the slope.Δy=Slope×Δx\Delta y = Slope \times \Delta xΔy=Slope×ΔxΔy=−23×3\Delta y = -\frac{2}{3} \times 3Δy=−32​×3

STEP 6

Simplify the calculation for Δy\Delta yΔy.Δy=−23×3=−2\Delta y = -\frac{2}{3} \times 3 = -2Δy=−32​×3=−2

STEP 7

Now we can find the coordinates of point B by adding Δx\Delta xΔx and Δy\Delta yΔy to the coordinates of point A.Bx=Ax+ΔxB_x = A_x + \Delta xBx​=Ax​+ΔxBy=Ay+ΔyB_y = A_y + \Delta yBy​=Ay​+Δy

STEP 8

Calculate the x-coordinate for point B.Bx=−1+3=2B_x = -1 + 3 = 2Bx​=−1+3=2

STEP 9

Calculate the y-coordinate for point B.By=−5−2=−7B_y = -5 - 2 = -7By​=−5−2=−7

STEP 10

Combine the x and y coordinates to get the coordinates of point B.Coordinates of point B=(2,−7)Coordinates\, of\, point\, B = (2, -7)CoordinatesofpointB=(2,−7)Another point on the line is (2,−7)(2, -7)(2,−7).

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For problem 12:
Assumptions
1. The coordinates of point A are $(-1, -5)$ .
2. The slope of the line is $-\frac{2}{3}$ .
3. We need to find the coordinates of another point B on the line.

The slope of a line is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line.
$Slope = \frac{\Delta y}{\Delta x}$

Using the given slope and the coordinates of point A, we can find the coordinates of another point B by choosing a value for $\Delta x$ and calculating the corresponding $\Delta y$ .
$-\frac{2}{3} = \frac{\Delta y}{\Delta x}$

Choose a convenient value for $\Delta x$ . Let's choose $\Delta x = 3$ since it will cancel out the denominator of the slope.
$\Delta x = 3$

Calculate the corresponding $\Delta y$ using the slope.
$\Delta y = Slope \times \Delta x$
$\Delta y = -\frac{2}{3} \times 3$

Simplify the calculation for $\Delta y$ .
$\Delta y = -\frac{2}{3} \times 3 = -2$

Now we can find the coordinates of point B by adding $\Delta x$ and $\Delta y$ to the coordinates of point A.
$B_x = A_x + \Delta x$
$B_y = A_y + \Delta y$

Calculate the x-coordinate for point B.
$B_x = -1 + 3 = 2$

Calculate the y-coordinate for point B.
$B_y = -5 - 2 = -7$

Combine the x and y coordinates to get the coordinates of point B.
$Coordinates\, of\, point\, B = (2, -7)$
Another point on the line is $(2, -7)$ .