Math / Algebra

QuestionA line passes through the points $(-4,-19)$ and $(12,-7)$ . Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that goes through two given points and write it in slope-intercept form, which looks like $y = mx + b$ . Watch out! Don't mix up the x and y coordinates when calculating the slope!
Also, remember that slope-intercept form is $y = mx + b$ , not $y = bx + m$ .

STEP 2

1. Calculate the slope.
2. Find the y-intercept.
3. Write the equation.

STEP 3

Let's label our points!
We'll call $(-4, -19)$ point 1, so $x_1 = -4$ and $y_1 = -19$ .
And we'll call $(12, -7)$ point 2, so $x_2 = 12$ and $y_2 = -7$ .

STEP 4

The slope ( $m$ ) is the change in y over the change in x.
The formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's plug in our values: $m = \frac{-7 - (-19)}{12 - (-4)}$ Notice the double negative becomes addition! $m = \frac{-7 + 19}{12 + 4}$ $m = \frac{12}{16}$ Now, we simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4: $m = \frac{12 \div 4}{16 \div 4}$ $m = \frac{3}{4}$ So, our slope is $m = \frac{3}{4}$ .

STEP 5

We know the slope-intercept form is $y = mx + b$ .
We've got m, and we can use one of our points to solve for b, the y-intercept.
Let's use point 1: $(-4, -19)$ .

STEP 6

Substitute the values into the equation: $-19 = \frac{3}{4}(-4) + b$ $-19 = -3 + b$ Now, we want to isolate b.
To do this, we can add 3 to both sides of the equation: $-19 + 3 = -3 + 3 + b$ $-16 = b$ So, our y-intercept is $b = -16$ .

STEP 7

We have our slope, $m = \frac{3}{4}$ , and our y-intercept, $b = -16$ .
Now we just plug them into the slope-intercept form: $y = \frac{3}{4}x - 16$

STEP 8

The equation of the line in slope-intercept form is $y = \frac{3}{4}x - 16$ .

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QuestionA line passes through the points $(-4,-19)$ and $(12,-7)$ . Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

Studdy Solution

STEP 1

STEP 2

1. Calculate the slope.
2. Find the y-intercept.
3. Write the equation.

STEP 3

Let's label our points!
We'll call $(-4, -19)$ point 1, so $x_1 = -4$ and $y_1 = -19$ .
And we'll call $(12, -7)$ point 2, so $x_2 = 12$ and $y_2 = -7$ .

STEP 4

STEP 5

We know the slope-intercept form is $y = mx + b$ .
We've got m, and we can use one of our points to solve for b, the y-intercept.
Let's use point 1: $(-4, -19)$ .

STEP 6

Substitute the values into the equation: $-19 = \frac{3}{4}(-4) + b$ $-19 = -3 + b$ Now, we want to isolate b.
To do this, we can add 3 to both sides of the equation: $-19 + 3 = -3 + 3 + b$ $-16 = b$ So, our y-intercept is $b = -16$ .

STEP 7

We have our slope, $m = \frac{3}{4}$ , and our y-intercept, $b = -16$ .
Now we just plug them into the slope-intercept form: $y = \frac{3}{4}x - 16$

STEP 8

The equation of the line in slope-intercept form is $y = \frac{3}{4}x - 16$ .

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QuestionA line passes through the points (−4,−19)(-4,-19)(−4,−19) and (12,−7)(12,-7)(12,−7). Write its equation in slope-intercept form.Write your answer using integers, proper fractions, and improper fractions in simplest form. □\square□

Studdy Solution

STEP 1

STEP 2

1. Calculate the slope.2. Find the y-intercept.3. Write the equation.

STEP 3

Let's **label** our points!We'll call (−4,−19)(-4, -19)(−4,−19) point 1, so x1=−4x_1 = -4x1​=−4 and y1=−19y_1 = -19y1​=−19.And we'll call (12,−7)(12, -7)(12,−7) point 2, so x2=12x_2 = 12x2​=12 and y2=−7y_2 = -7y2​=−7.

STEP 4

STEP 5

We know the slope-intercept form is y=mx+by = mx + by=mx+b.We've got *m*, and we can use one of our points to solve for *b*, the **y-intercept**.Let's use point 1: (−4,−19)(-4, -19)(−4,−19).

STEP 6

STEP 7

We have our **slope**, m=34m = \frac{3}{4}m=43​, and our **y-intercept**, b=−16b = -16b=−16.Now we just plug them into the slope-intercept form: y=34x−16 y = \frac{3}{4}x - 16 y=43​x−16

STEP 8

The equation of the line in slope-intercept form is y=34x−16y = \frac{3}{4}x - 16y=43​x−16.

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QuestionA line passes through the points $(-4,-19)$ and $(12,-7)$ . Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

1. Calculate the slope.
2. Find the y-intercept.
3. Write the equation.

Let's label our points!
We'll call $(-4, -19)$ point 1, so $x_1 = -4$ and $y_1 = -19$ .
And we'll call $(12, -7)$ point 2, so $x_2 = 12$ and $y_2 = -7$ .

We know the slope-intercept form is $y = mx + b$ .
We've got m, and we can use one of our points to solve for b, the y-intercept.
Let's use point 1: $(-4, -19)$ .

We have our slope, $m = \frac{3}{4}$ , and our y-intercept, $b = -16$ .
Now we just plug them into the slope-intercept form: $y = \frac{3}{4}x - 16$

The equation of the line in slope-intercept form is $y = \frac{3}{4}x - 16$ .