Question

unit 5 test
what is the slope-intercept form of the equation of the line containing the points $(-2, 4)$ and $(6, 0)$?
$y = -\frac{1}{2}x + 5$
$y = \frac{1}{2}x + 5$
$y = -\frac{1}{2}x + 3$
$y = -\frac{1}{2}x + 8$

Explanation:

Step1: Calculate the slope

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(-2,4)$ and $(6,0)$:
$m=\frac{0-4}{6-(-2)}=\frac{-4}{8}=-\frac{1}{2}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=-\frac{1}{2}$ and point $(6,0)$:
$0=-\frac{1}{2}(6)+b$
$0=-3+b$
$b=3$

Step3: Write final equation

Combine $m=-\frac{1}{2}$ and $b=3$ into $y=mx+b$:
$y=-\frac{1}{2}x+3$

Answer:

$y = -\frac{1}{2}x + 3$