Question

a line has a slope of $-\frac{4}{5}$ and passes through the point (-12, 9). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m=-\frac{4}{5}$ and the line passes through the point $(-12,9)$. Substitute $x=-12$, $y = 9$ and $m=-\frac{4}{5}$ into the equation $y=mx + b$.
$9=-\frac{4}{5}\times(-12)+b$

Step2: Simplify the right - hand side

First, calculate $-\frac{4}{5}\times(-12)=\frac{48}{5}$. So the equation becomes $9=\frac{48}{5}+b$.

Step3: Solve for $b$

Subtract $\frac{48}{5}$ from both sides. We rewrite $9$ as $\frac{45}{5}$. Then $b=\frac{45}{5}-\frac{48}{5}=-\frac{3}{5}$.

Step4: Write the equation of the line

Now that we have $m = -\frac{4}{5}$ and $b=-\frac{3}{5}$, the equation of the line in slope - intercept form is $y=-\frac{4}{5}x-\frac{3}{5}$.

Answer:

$y = -\frac{4}{5}x-\frac{3}{5}$