Question

near relationships mini retest
speak options zoom add n

1. the graph of a linear function passes through the points (-2,70) and (6,-50).

which equation represents the function?
$y = -\frac{3}{2}x + 40$
$y = -\frac{3}{2}x + 4$
$y = -15x + 4$
$y = -15x + 40$
clear all

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(-2,70)$ and $(x_2,y_2)=(6, - 50)$. So $m=\frac{-50 - 70}{6-(-2)}=\frac{-120}{8}=-15$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Let's use the point $(-2,70)$ and $m=-15$. So $y - 70=-15(x+2)$. Expand: $y - 70=-15x-30$. Add 70 to both sides: $y=-15x + 40$.

Answer:

$y=-15x + 40$