Question

so the table represents some points on the graph of a linear function.

x	y
-20	-268
-14	-196
-8	-124
-1	-40

which equation represents the same relationship?
f y + 268 = \frac{1}{12}(x + 20)
g y + 20 = \frac{1}{12}(x + 268)
h y + 268 = 12(x + 20)
j y + 20 = 12(x + 268)

Explanation:

Step1: Find the slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the first two - points $(-20,-268)$ and $(-14,-196)$.
$m=\frac{-196-(-268)}{-14 - (-20)}=\frac{-196 + 268}{-14 + 20}=\frac{72}{6}=12$.

Step2: Use the point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Using the point $(-20,-268)$ and $m = 12$, we get $y-(-268)=12(x - (-20))$, which simplifies to $y + 268=12(x + 20)$.

Answer:

H. $y + 268=12(x + 20)$