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 $(2,8)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{8-6}{2-0}=\frac{2}{2}=1$

Step3: Substitute into slope-intercept form

Slope-intercept form: $y=mx+b$
Substitute $m=1$, $b=6$: $y=1x+6$

Step4: Simplify the equation

$y=x+6$

Answer:

$y=x+6$