➕ Algebra 1 · Linear Functions
Parallel and Perpendicular Lines: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
Two different non-vertical lines with the same slope are parallel.
✓ True. With the same slope and different y-intercepts, the lines never meet. (Different lines with the same slope must have different y-intercepts.)
The lines y = 7x + 1 and 14x − 2y = −2 are parallel.
✗ False. Solve the second for y: −2y = −14x − 2, so y = 7x + 1. Both equations describe the same line, so it is not a pair of parallel lines.
A line with slope 9 is perpendicular to a line with slope −9.
✗ False. 9 × (−9) = −81, not −1. The perpendicular slope is −1/9.
A line with slope 3/10 is perpendicular to a line with slope −10/3.
✓ True. (3/10)(−10/3) = −1. The slopes are negative reciprocals.
A line with slope 1/6 is perpendicular to a line with slope 6.
✗ False. (1/6)(6) = 1, not −1. The sign change is missing. The perpendicular slope is −6.
The line x = 9 is perpendicular to the line y = −4.
✓ True. x = 9 is vertical and y = −4 is horizontal. A vertical line and a horizontal line cross at a right angle.
Every line perpendicular to a horizontal line is vertical.
✓ True. A horizontal line has slope 0. The only lines that cross it at a right angle are the vertical lines.
The slope of the line 5x + 2y = 10 is 5.
✗ False. Solve for y: 2y = −5x + 10, so y = −(5/2)x + 5. The slope is −5/2.
If the slopes of two lines multiply to −1, the lines are perpendicular.
✓ True. A product of −1 means each slope is the negative reciprocal of the other, which is the condition for perpendicular lines.
Two perpendicular lines can both have positive slopes.
✗ False. The product of two positive numbers is positive, never −1. Of two perpendicular slanted lines, one slope is positive and the other negative. (A horizontal line has slope 0 and a vertical line has an undefined slope, so neither is positive.)
Two different vertical lines are parallel.
✓ True. They never meet. Their slopes are both undefined, but the lines are clearly parallel.
Two lines with different slopes never meet.
✗ False. Two non-vertical lines with different slopes meet at exactly one point. Only parallel lines never meet.
The line through (3, 4) that is parallel to y = 6x + 9 is y = 6x − 14.
✓ True. The slope stays 6. Substitute (3, 4): 4 = 6(3) + b, so b = −14. Check: 6(3) − 14 = 4.
The line through (4, 0) that is perpendicular to y = 2x is y = −2x + 8.
✗ False. The line y = −2x + 8 does pass through (4, 0), but its slope is −2, and 2 × (−2) = −4, not −1. The perpendicular slope is −1/2, so the line is y = −(1/2)x + 2.