Question

a line has a slope of $-\frac{1}{5}$ and passes through the point $(-5, 9)$. what is its equation in point - slope form?\
use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.\
$y - \square = \square(x - \square)$

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Step2: Identify $m$, $x_1$, and $y_1$

We are given that the slope $m =-\frac{1}{5}$ and the point $(x_1,y_1)=(- 5,9)$. So $x_1=-5$ and $y_1 = 9$.

Step3: Substitute into the formula

Substitute $m =-\frac{1}{5}$, $x_1=-5$ and $y_1 = 9$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y - 9=-\frac{1}{5}(x-(-5))$, which simplifies to $y - 9=-\frac{1}{5}(x + 5)$

Answer:

$y - 9=-\frac{1}{5}(x+5)$ (or in the boxed form as per the problem's blanks: $y - \boldsymbol{9}=\boldsymbol{-\frac{1}{5}}(x-\boldsymbol{(-5)})$ but since the problem has $x - \square$, we can rewrite $x-(-5)$ as $x + 5$, but following the blank structure $y - 9=-\frac{1}{5}(x-(-5))$ so the blanks are filled with 9, $-\frac{1}{5}$, and - 5 respectively)