Question

write the equation of the line in fully simplified slope - intercept form

Explanation:

Step1: Identify two points

From the graph, pick two clear points: $(x_1,y_1)=(0,6)$ and $(x_2,y_2)=(8,12)$

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{12-6}{8-0}=\frac{6}{8}=\frac{3}{4}$

Step3: Identify y-intercept

The line crosses the y-axis at $(0,6)$, so $b=6$

Step4: Write slope-intercept form

Use $y=mx+b$
$y=\frac{3}{4}x+6$

Answer:

$y=\frac{3}{4}x+6$