Question

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

Explanation:

Step1: Find the y - intercept

The line crosses the y - axis at (0, 4), so $b = 4$.

Step2: Find two points on the line

Let's take (0, 4) and (4, 0).

Step3: Calculate the slope $m$

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, with $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(4,0)$, we have $m=\frac{0 - 4}{4-0}=\frac{-4}{4}=- 1$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substituting $m=-1$ and $b = 4$, we get $y=-x + 4$.

Answer:

$y=-x + 4$