Question

a line passes through the point $(-8, -7)$ and has a slope of $\frac{5}{4}$. write an equation in slope - intercept form for this line.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line. Here, $x_1=-8$, $y_1 = - 7$ and $m=\frac{5}{4}$.
Substitute these values into the point - slope form: $y-(-7)=\frac{5}{4}(x - (-8))$.
Simplify the left - hand side and the right - hand side: $y + 7=\frac{5}{4}(x + 8)$.

Step2: Convert to slope - intercept form

Slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
First, distribute $\frac{5}{4}$ on the right - hand side: $y+7=\frac{5}{4}x+\frac{5}{4}\times8$.
Calculate $\frac{5}{4}\times8$: $\frac{5\times8}{4}=10$. So the equation becomes $y + 7=\frac{5}{4}x+10$.
Then, subtract 7 from both sides to solve for $y$: $y=\frac{5}{4}x+10 - 7$.
Simplify $10 - 7$: $y=\frac{5}{4}x + 3$.

Answer:

$y=\frac{5}{4}x + 3$