Question

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

Explanation:

Step1: Identify two points

Choose points $(-2, 11)$ and $(1, -7)$ from the line.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$$m=\frac{-7-11}{1-(-2)}=\frac{-18}{3}=-6$$

Step3: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=-6$ and point $(0, -1)$ (the y-intercept on the graph):
$$-1 = -6(0)+b \implies b=-1$$

Step4: Write the equation

Substitute $m=-6$ and $b=-1$ into $y=mx+b$.

Answer:

$y = -6x - 1$