Question

determine the equation, in slope-intercept form, for the line shown in the graph below:

Explanation:

Step1: Identify two points on line

The line passes through $(2, -4)$ and $(0, -3)$.

Step2: Calculate the slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-3 - (-4)}{0 - 2}=\frac{1}{-2}=-\frac{1}{2}$

Step3: Find y-intercept $b$

The line crosses the y-axis at $(0, -3)$, so $b=-3$.

Step4: Write slope-intercept equation

Slope-intercept form is $y=mx+b$. Substitute $m=-\frac{1}{2}$ and $b=-3$.
$y=-\frac{1}{2}x - 3$

Answer:

$y=-\frac{1}{2}x - 3$