Question

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

Explanation:

Step1: Identify intercept and points

The y-intercept $b$ is 4 (where the line crosses the y-axis). We pick two points on the line: $(0, 4)$ and $(6, 5)$.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{5-4}{6-0}=\frac{1}{6}$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{1}{6}$ and $b=4$.
$y=\frac{1}{6}x+4$

Answer:

$y=\frac{1}{6}x+4$