Question: Determine whether the pair of lines is parallel, perpendicular, or neither. $$x - 5y = -8$$ $$y =…

Determine whether the pair of lines is parallel, perpendicular, or neither.

$$x - 5y = -8$$ $$y = 3x - 2$$

Choose the correct answer below.

A. The two lines are perpendicular. B. The two lines are neither parallel nor perpendicular. C. The two lines are parallel. D. More information is needed.

Solution

To determine whether the lines are parallel, perpendicular, or neither, we need to compare their slopes. First, let’s write each equation in the form \( y = mx + b \), where \( m \) is the slope. Starting with the first equation: \( x - 5y = -8 \) Solve for \( y \): Add \( 5y \) to both sides: \[ x = 5y - 8 \] Add 8 to both sides: \[ x + 8 = 5y \] Divide by 5: \[ y = \frac{1}{5}x + \frac{8}{5} \] The slope of the first line is \( \frac{1}{5} \). Now, for the second equation: \( y = 3x - 2 \) This is already in slope-intercept form, with the slope being 3. Since the slopes \(\frac{1}{5}\) and 3 are neither equal nor negative reciprocals of each other, the lines are neither parallel nor perpendicular. The correct answer is: B. The two lines are neither parallel nor perpendicular.