Question

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

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. The line passes through $(0,5)$ and $(- 8,0)$. So $m=\frac{5 - 0}{0-(-8)}=\frac{5}{8}$.

Step2: Identify the y - intercept

The y - intercept $b$ is the y - value when $x = 0$. From the graph, when $x = 0$, $y=5$, so $b = 5$.

Step3: Write the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m=\frac{5}{8}$ and $b = 5$ into the equation, we get $y=\frac{5}{8}x+5$.

Answer:

$y=\frac{5}{8}x + 5$