Question

write the equation of this line in slope-intercept form.

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 5)$, so $b=5$.

Step2: Calculate slope

Use two points $(0,5)$ and $(4,4)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4-5}{4-0}=\frac{-1}{4}=-\frac{1}{4}$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-\frac{1}{4}$ and $b=5$.

Answer:

$y=-\frac{1}{4}x+5$