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 $(0,6)$, so $b=6$.

Step2: Calculate slope using two points

Use points $(0,6)$ and $(10,10)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{10-6}{10-0}=\frac{4}{10}=\frac{2}{5}$

Step3: Write slope-intercept form

Slope-intercept form: $y=mx+b$, substitute $m=\frac{2}{5}$ and $b=6$.

Answer:

$y=\frac{2}{5}x+6$