Question

find the slope of a line parallel to the line whose equation is 12x - 15y = 315. fully simplify your answer.

Explanation:

Step1: Rewrite the equation in slope - intercept form ($y = mx + b$)

We start with the equation $12x-15y = 315$. We want to solve for $y$.
First, subtract $12x$ from both sides of the equation:
$-15y=-12x + 315$

Step2: Solve for $y$

Divide every term in the equation by $- 15$:
$y=\frac{-12x}{-15}+\frac{315}{-15}$
Simplify each term:
$\frac{-12x}{-15}=\frac{12x}{15}=\frac{4x}{5}$ (by dividing numerator and denominator by 3)
$\frac{315}{-15}=- 21$
So, the equation of the line in slope - intercept form is $y=\frac{4}{5}x-21$.
The slope of a line in the form $y = mx + b$ is $m$. For the line $y=\frac{4}{5}x - 21$, the slope $m=\frac{4}{5}$.
Parallel lines have the same slope. So, the slope of a line parallel to the line $12x - 15y=315$ is also $\frac{4}{5}$.

Answer:

$\frac{4}{5}$