Question

question
find the slope of a line parallel to the line whose equation is ( 15x - 6y = 54 ). fully simplify your answer.

Explanation:

Step1: Rewrite in slope - intercept form

We know that the slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We start with the equation \(15x-6y = 54\).
First, we want to solve for \(y\). Subtract \(15x\) from both sides of the equation:
\(-6y=-15x + 54\)

Step2: Solve for y

Divide every term in the equation \(-6y=-15x + 54\) by \(-6\) to isolate \(y\):
\(y=\frac{-15x}{-6}+\frac{54}{-6}\)
Simplify each term: \(\frac{-15x}{-6}=\frac{5x}{2}\) and \(\frac{54}{-6}=-9\). So the equation of the line in slope - intercept form is \(y=\frac{5}{2}x-9\).

Step3: Determine the slope of the parallel line

The slope of a line in the form \(y = mx + b\) is \(m\). For the line \(y=\frac{5}{2}x - 9\), the slope \(m=\frac{5}{2}\).
Parallel lines have the same slope. So the slope of a line parallel to the line \(15x - 6y=54\) is also \(\frac{5}{2}\).

Answer:

\(\frac{5}{2}\)