Question

a line has a slope of -\frac{4}{5} and passes through the point (-11, 10). 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 $m=-\frac{4}{5}$, so the equation is $y =-\frac{4}{5}x + b$.

Step2: Substitute the point into the equation

Substitute $x=-11$ and $y = 10$ into $y=-\frac{4}{5}x + b$. We get $10=-\frac{4}{5}\times(-11)+b$.

Step3: Simplify the right - hand side

$-\frac{4}{5}\times(-11)=\frac{44}{5}$, so the equation becomes $10=\frac{44}{5}+b$.

Step4: Solve for $b$

Subtract $\frac{44}{5}$ from both sides. $b = 10-\frac{44}{5}=\frac{50}{5}-\frac{44}{5}=\frac{50 - 44}{5}=\frac{6}{5}$.

Step5: Write the final equation

The equation of the line in slope - intercept form is $y=-\frac{4}{5}x+\frac{6}{5}$.

Answer:

$y =-\frac{4}{5}x+\frac{6}{5}$