Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –x + 10
–2x + 8y = 6
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.