Question

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

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation 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.

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

We are given that the line passes through the point $(-8,-8)$, so $x_1=-8$ and $y_1 = - 8$. The slope $m=\frac{5}{4}$.

Step3: Substitute values into the formula

Substitute $x_1=-8$, $y_1=-8$ and $m = \frac{5}{4}$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y-(-8)=\frac{5}{4}(x - (-8))$, which simplifies to $y + 8=\frac{5}{4}(x + 8)$.

Answer:

$y + 8=\frac{5}{4}(x + 8)$