Question

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

Explanation:

Step1: Identify slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Pick two points from graph

Choose $(0,6)$ and $(-6,0)$.

Step3: Calculate the slope

$m=\frac{0-6}{-6-0}=\frac{-6}{-6}=1$

Step4: Identify y-intercept

The line crosses the y-axis at $(0,6)$, so $b=6$.

Step5: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=1$ and $b=6$.

Answer:

$y=x+6$