Question

consider the line $-5x - 9y = 8$. what is the slope of a line perpendicular to this line? what is the slope of a line parallel to this line? your answer slope of a perpendicular line: slope of a parallel line:

Explanation:

Step1: Convert to slope - intercept form

The equation of the line is \(-5x - 9y=8\). We want to write it in the form \(y = mx + b\), where \(m\) is the slope.
First, we solve for \(y\):
\(-9y=5x + 8\) (Add \(5x\) to both sides of the equation)
\(y=-\frac{5}{9}x-\frac{8}{9}\) (Divide both sides by \(- 9\))

Step2: Find the slope of the parallel line

Parallel lines have the same slope. From the equation \(y =-\frac{5}{9}x-\frac{8}{9}\), the slope \(m\) of the given line is \(-\frac{5}{9}\). So the slope of a line parallel to this line is also \(-\frac{5}{9}\).

Step3: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is \(- 1\). Let the slope of the perpendicular line be \(m_{perp}\). We know that \(m\times m_{perp}=-1\), where \(m =-\frac{5}{9}\).
So, \(-\frac{5}{9}\times m_{perp}=-1\)
\(m_{perp}=\frac{-1}{-\frac{5}{9}}=\frac{9}{5}\) (Multiply both sides by \(-\frac{9}{5}\))

Answer:

Slope of a perpendicular line: \(\frac{9}{5}\)
Slope of a parallel line: \(-\frac{5}{9}\)