Question

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

Explanation:

Step1: Identify y-intercept

The y-intercept $b$ is where the line crosses the y-axis, so $b=4$.

Step2: Calculate slope $m$

Use two points $(0,4)$ and $(2,-1)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-1-4}{2-0}=\frac{-5}{2}$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m$ and $b$.
$y=-\frac{5}{2}x+4$

Answer:

$y=-\frac{5}{2}x+4$