Question

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

Explanation:

Step1: Identify y-intercept

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

Step2: Calculate slope

Use two points: $(0, -3)$ and $(2, -4)$.
Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-4 - (-3)}{2 - 0} = \frac{-1}{2}$

Step3: Write slope-intercept form

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

Answer:

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