QuestionFind the equation of the linear function containing the Show your w points $(2,-4)$ and $(-1,-7)$ . Submit your answer in slopeintercept form, or $y=m x+b$ .

Studdy Solution

STEP 1

1. We are given two points: $(2, -4)$ and $(-1, -7)$ .
2. We need to find the equation of the linear function passing through these points.
3. The equation should be in slope-intercept form: $y = mx + b$ .

STEP 2

1. Calculate the slope $m$ of the line.
2. Use the slope and one of the points to find the y-intercept $b$ .
3. Write the equation in slope-intercept form.

STEP 3

To find the slope $m$ , use the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(2, -4)$ and $(-1, -7)$ into the formula:
$m = \frac{-7 - (-4)}{-1 - 2} = \frac{-7 + 4}{-1 - 2} = \frac{-3}{-3} = 1$

STEP 4

Now that we have the slope $m = 1$ , use one of the points to find the y-intercept $b$ . Let's use the point $(2, -4)$ .
Substitute $m = 1$ , $x = 2$ , and $y = -4$ into the slope-intercept form $y = mx + b$ :
$-4 = 1 \cdot 2 + b$
Solve for $b$ :
$-4 = 2 + b \\ b = -4 - 2 \\ b = -6$

STEP 5

Now that we have both the slope $m = 1$ and the y-intercept $b = -6$ , we can write the equation of the line in slope-intercept form:
$y = 1x - 6$
Simplify to:
$y = x - 6$
The equation of the linear function is:
$\boxed{y = x - 6}$

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