Question

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

Explanation:

Step1: Identify two points on the line

The line passes through points $(0,8)$ and $(4,0)$.

Step2: Calculate the slope $m$

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,8)$ and $(x_2,y_2)=(4,0)$. Then $m=\frac{0 - 8}{4-0}=\frac{-8}{4}=- 2$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,8)$, $b = 8$.

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m=-2$ and $b = 8$ gives $y=-2x + 8$.

Answer:

$y=-2x + 8$