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 $(0, -8)$, so $b = -8$.

Step2: Calculate slope using two points

Use points $(0, -8)$ and $(2, -9)$. Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-9 - (-8)}{2 - 0} = \frac{-1}{2}$

Step3: Write slope-intercept form

Substitute $m$ and $b$ into $y = mx + b$.
$y = -\frac{1}{2}x - 8$

Answer:

$y = -\frac{1}{2}x - 8$