Question

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

Explanation:

Step1: Identify intercept and a point

The y-intercept $b$ is $-6$ (where the line crosses the y-axis). A point on the line is $(5, -9)$.

Step2: Calculate the slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Let $(x_1,y_1)=(0,-6)$ and $(x_2,y_2)=(5,-9)$.
$$m=\frac{-9 - (-6)}{5 - 0}=\frac{-3}{5}$$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-\frac{3}{5}$ and $b=-6$.
$$y=-\frac{3}{5}x - 6$$

Answer:

$y=-\frac{3}{5}x - 6$