Question

a line has a slope of $-\frac{1}{5}$ and passes through the point $(-5, 7)$. write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. We know that $m =-\frac{1}{5}$ and the point is $(-5,7)$, so $x_1=-5$ and $y_1 = 7$.
Substitute these values into the point - slope form: $y - 7=-\frac{1}{5}(x - (-5))$, which simplifies to $y - 7=-\frac{1}{5}(x + 5)$.

Step2: Convert to slope - intercept form ($y=mx + b$)

Expand the right - hand side: $y - 7=-\frac{1}{5}x-1$.
Then, add 7 to both sides of the equation to solve for $y$: $y=-\frac{1}{5}x-1 + 7$.
Simplify the constant terms: $y=-\frac{1}{5}x+6$.

Answer:

$y = -\frac{1}{5}x + 6$