Question

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

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 7)$, so $b=7$.

Step2: Calculate slope using two points

Use points $(0,7)$ and $(4,0)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{0-7}{4-0}=-\frac{7}{4}$

Step3: Plug into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-\frac{7}{4}$ and $b=7$.
$y=-\frac{7}{4}x+7$

Answer:

$y=-\frac{7}{4}x+7$