Question

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

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -2)$, so $b = -2$.

Step2: Calculate slope using two points

Use points $(0, -2)$ and $(2, 1)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{1-(-2)}{2-0}=\frac{3}{2}$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{3}{2}$ and $b=-2$.

Answer:

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