To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two equations.
Given equations:
1. y = -4x + 3
2. -2x + 8y = 5
First, rewrite Equation 2 in slope-intercept form (y = mx + b):
-2x + 8y = 5
8y = 2x + 5
y = 1/4x + 5/8
Now we can see that the slope of Equation 1 is -4, and the slope of Equation 2 is 1/4. Since the slopes are negative reciprocals of each other (opposite signs and inverse), the lines are perpendicular.
Therefore, the lines described by the given equations are perpendicular. The correct response is:
b. perpendicular
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –4x + 3
–2x + 8y = 5
(1 point)
Responses
a. parallel
b. perpendicular
c. neither
1 answer