Question

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

Explanation:

Step1: Identify the y - intercept

The line crosses the y - axis at the point $(0,8)$, so $b = 8$.

Step2: Calculate the slope

Pick two points on the line, say $(0,8)$ and $(1,4)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 8,x_2=1,y_2 = 4$. Then $m=\frac{4 - 8}{1-0}=\frac{-4}{1}=-4$.

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m=-4$ and $b = 8$ into the equation, we get $y=-4x + 8$.

Answer:

$y=-4x + 8$