Question

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

x	y
- 4	10
- 2	?
6	- 5

which function represents the relationship?
a (y=-\frac{3}{2}x + 4)
b (y =-\frac{3}{2}x-14)
c (y=-\frac{3}{2}x - 2)
d (y=-\frac{3}{2}x-1)

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-4,10)$ and $(x_2,y_2)=(6, - 5)$.
$m=\frac{-5 - 10}{6-(-4)}=\frac{-15}{10}=-\frac{3}{2}$

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(-4,10)$ and $m =-\frac{3}{2}$.
$y - 10=-\frac{3}{2}(x + 4)$
$y-10=-\frac{3}{2}x-6$
$y=-\frac{3}{2}x + 4$

Answer:

A. $y=-\frac{3}{2}x + 4$