Question

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

Explanation:

Step1: Identify slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Pick two points on line

Use $(0, -2)$ and $(2, -4)$

Step3: Calculate the slope

$m = \frac{-4 - (-2)}{2 - 0} = \frac{-2}{2} = -1$

Step4: Identify y-intercept

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

Step5: Write slope-intercept form

Slope-intercept form is $y = mx + b$

Answer:

$y = -x - 2$