Question

a line has a slope of -\frac{2}{3} and passes through the point (17, -6). 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 are given $m=-\frac{2}{3}$ and the point $(x = 17,y=-6)$.

Step2: Substitute values into the equation

Substitute $x = 17$, $y=-6$ and $m =-\frac{2}{3}$ into $y=mx + b$. We get $-6=-\frac{2}{3}\times17 + b$.

Step3: Solve for $b$

First, calculate $-\frac{2}{3}\times17=-\frac{34}{3}$. Then the equation becomes $-6=-\frac{34}{3}+b$. Add $\frac{34}{3}$ to both sides: $b=-6+\frac{34}{3}$. Rewrite $-6$ as $-\frac{18}{3}$, so $b=-\frac{18}{3}+\frac{34}{3}=\frac{-18 + 34}{3}=\frac{16}{3}$.

Step4: Write the equation of the line

Substitute $m =-\frac{2}{3}$ and $b=\frac{16}{3}$ into $y=mx + b$. The equation is $y=-\frac{2}{3}x+\frac{16}{3}$.

Answer:

$y =-\frac{2}{3}x+\frac{16}{3}$