Question

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

Explanation:

Step1: Identify two points

From the graph, we can pick two clear points on the line: $(0, -2)$ and $(3, 1)$.

Step2: Calculate the slope

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

Step3: Find y-intercept

The y-intercept $b$ is the y-value when $x=0$, which is $-2$ (from the point $(0, -2)$).

Step4: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=1$ and $b=-2$.
$y=1x-2$ which simplifies to $y=x-2$.

Answer:

$y = x - 2$