Question

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = -4x + 3
-2x + 8y = 5
(1 point)
O parallel
perpendicular
neither

Answer 1

To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines.

First, let's find the slope of the first equation, y = -4x + 3.

The first equation is written in slope-intercept form y = mx + b, where m represents the slope of the line.

Comparing the equation y = -4x + 3 to y = mx + b, we can see that the slope, m, is -4.

Now, let's find the slope of the second equation, -2x + 8y = 5.

To find the slope, we need to rewrite the second equation in slope-intercept form.

-2x + 8y = 5
8y = 2x + 5
y = (2/8)x + 5/8
y = (1/4)x + 5/8

Comparing the equation y = (1/4)x + 5/8 to y = mx + b, we can see that the slope, m, is 1/4.

Now that we have the slopes of both lines, we can compare them.

The slope of the first equation is -4.
The slope of the second equation is 1/4.

Since the slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
Therefore, the correct answer is neither.