Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –one fourthx + 10
–2x + 8y = 6
(1 point)
To determine the relationship between the two lines, we need to rewrite the second equation in slope-intercept form (y = mx + b), where m is the slope.
First, solve for y in the second equation:
-2x + 8y = 6
8y = 2x + 6
y = (2/8)x + 6/8
y = (1/4)x + 3/4
Now, we can see that the slope of the first equation is -1/4, while the slope of the second equation is 1/4. Since the slopes are negative reciprocals of each other, the lines are perpendicular to each other.