Question

Indicate whether the lines are parallel, perpendicular, or neither and explain why.

-2x + 8y = 9 and x - 4y = 21
a) Parallel
b) Perpendicular
c) Neither
d) None of the above

Answer 1

The lines -2x + 8y = 9 and x - 4y = 21 are parallel.

Step-by-step explanation:

The given equations are -2x + 8y = 9 and x - 4y = 21. To determine whether the lines are parallel, perpendicular, or neither, we need to analyze their slopes. Rewrite the equations into slope-intercept form, y = mx + b. Equation 1 becomes y = (1/4)x - (21/4), and Equation 2 becomes y = (1/4)x + (9/8). From the equations, we can see that the slopes of both lines are equal, which means the lines are parallel to each other.