Question

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

Explanation:

Step1: Find the slope

The slope $m$ of a line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can take two points on the line, say $(0,8)$ and $(- 12,0)$. Then $m=\frac{8 - 0}{0-(-12)}=\frac{8}{12}=\frac{2}{3}$.

Step2: Identify the y - intercept

The y - intercept $b$ is the y - value when $x = 0$. From the graph, when $x = 0$, $y=8$, so $b = 8$.

Step3: Write the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m=\frac{2}{3}$ and $b = 8$ into the formula, we get $y=\frac{2}{3}x+8$.

Answer:

$y=\frac{2}{3}x + 8$