Question

a line has a slope of $-\frac{1}{8}$ and passes through the point $(-8, 7)$. write its equation in slope - intercept form. help 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 $m=-\frac{1}{8}$ and the line passes through the point $(- 8,7)$. Substitute $m =-\frac{1}{8}$, $x=-8$ and $y = 7$ into the equation $y=mx + b$.
So we have $7=-\frac{1}{8}\times(-8)+b$.

Step2: Solve for $b$

First, calculate $-\frac{1}{8}\times(-8)=1$. Then the equation becomes $7 = 1 + b$. Subtract 1 from both sides of the equation: $b=7 - 1=6$.

Step3: Write the equation

Since $m =-\frac{1}{8}$ and $b = 6$, the equation of the line in slope - intercept form is $y=-\frac{1}{8}x+6$.

Answer:

$y =-\dfrac{1}{8}x + 6$