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 $(0, -1)$, so $b = -1$.

Step2: Calculate slope using two points

Use points $(0, -1)$ and $(3, -4)$. Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-4 - (-1)}{3 - 0} = \frac{-3}{3} = -1$

Step3: Substitute into slope-intercept form

Slope-intercept form is $y = mx + b$. Substitute $m=-1$, $b=-1$.
$y = -1x - 1$

Answer:

$y = -x - 1$