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 $(0, 5)$, so $b=5$.

Step2: Calculate slope using two points

Use points $(0,5)$ and $(1,-1)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-1-5}{1-0}=\frac{-6}{1}=-6$

Step3: Substitute into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-6$, $b=5$.

Answer:

$y=-6x+5$