Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
x + 5y = –20
y = –7/8x – 1
32x – 28y = –36
parallel
perpendicular
neither
I think it's perpendicular - asked this question earlier but didn't get a definite response...thanks
yes, the two lines
y = -7/8 x - 1 and
32x - 28y = -36 are perpendicular.
what if the slope is the same
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the equations.
For the first pair of equations:
1) Convert the first equation to slope-intercept form (y = mx + b):
x + 5y = –20
5y = –x - 20
y = -(1/5)x - 4
2) Compare the slopes. The slope of the first equation is -1/5, while the slope of the second equation is -7/8. Since these slopes are not the same, the lines are neither parallel nor perpendicular.
For the second pair of equations:
1) Convert the second equation to slope-intercept form (y = mx + b):
32x – 28y = –36
-28y = -32x - 36
y = (32/28)x + 36/28
simplify => y = (8/7)x + 9/7
2) Compare the slopes. The slope of the first equation is 8/7, while the slope of the second equation is -7/8 (this was mentioned in your previous question). Since the product of these slopes is -1 (m1 * m2 = (8/7) * (-7/8) = -1), the lines are perpendicular.
Therefore, the first pair of equations has neither parallel nor perpendicular lines, while the second pair of equations has perpendicular lines.