Question

find the slope of a line parallel to the line whose equation is $5x - 3y = 18$. fully simplify your answer.

Explanation:

Step1: Rewrite in slope - intercept form

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 \(5x-3y = 18\).
First, we want to solve for \(y\). Subtract \(5x\) from both sides of the equation:
\(-3y=-5x + 18\)

Step2: Solve for y

Divide every term in the equation \(-3y=-5x + 18\) by \(-3\) to isolate \(y\):
\(y=\frac{-5x}{-3}+\frac{18}{-3}\)
Simplify the fractions:
\(y=\frac{5}{3}x-6\)

Step3: Determine the slope of parallel line

Parallel lines have the same slope. The slope of the line \(y = \frac{5}{3}x-6\) is \(\frac{5}{3}\), so the slope of a line parallel to it is also \(\frac{5}{3}\).

Answer:

\(\frac{5}{3}\)