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 $(-10, 1)$ and $(0, 5)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{5-1}{0-(-10)}=\frac{4}{10}=\frac{2}{5}$

Step3: Plug into slope-intercept form

Slope-intercept form: $y=mx+b$
Substitute $m=\frac{2}{5}$ and $b=5$.

Answer:

$y=\frac{2}{5}x+5$