Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points

Choose points $(2, -2)$ and $(5, 4)$ from the line.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4-(-2)}{5-2}=\frac{6}{3}=2$

Step3: Find y-intercept

Substitute $m=2$, $(x,y)=(2,-2)$ into $y=mx+b$:
$-2=2(2)+b$
$-2=4+b$
$b=-2-4=-6$

Step4: Write slope-intercept form

Substitute $m=2$ and $b=-6$ into $y=mx+b$
$y=2x-6$

Answer:

$y=2x-6$