Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

Question

y = –x + 10

–2x + 8y = 6

Answer 1

To determine the relationship between the lines for the given pair of equations, let's first convert the second equation into slope-intercept form (y = mx + b), where m represents the slope of the line:

–2x + 8y = 6
8y = 2x + 6
y = (2/8)x + (6/8)
y = (1/4)x + 3/4

Now we can compare the slopes of the two lines:

The slope of the first line (y = -x + 10) is -1.
The slope of the second line (y = (1/4)x + 3/4) is 1/4.

Since the slopes of the two lines are negative reciprocals (opposite signs and inverted), the lines are perpendicular.