➕ Algebra 1 · Linear Functions
Parallel and Perpendicular Lines flashcards
Say the answer out loud before you flip. Cards you miss come back sooner; cards you know come back later. That spacing is what builds long-term memory.
All 15 flashcards at a glance
Card 1
What do non-vertical parallel lines have in common, and how do they differ?
They have the same slope and different y-intercepts, so they never meet. The same slope and the same y-intercept would be the same line.
Card 2
How are the slopes of two perpendicular lines related, if neither line is horizontal or vertical?
They are negative reciprocals, so their product is −1.
Card 3
What is the slope of a line perpendicular to a line with slope 4/9?
−9/4. Flip 4/9 to get 9/4, then change the sign. Check: (4/9)(−9/4) = −1.
Card 4
What is the slope of a line perpendicular to a line with slope −7?
1/7. Write −7 as −7/1, flip to get 1/(−7) = −1/7, then change the sign to get 1/7. Check: (−7)(1/7) = −1.
Card 5
What kind of line is perpendicular to the horizontal line y = −6?
A vertical line, x = a for some number a. A horizontal line has slope 0, and 0 has no reciprocal, so use the picture instead of the rule.
Card 6
Parallel, perpendicular or neither: y = −3x + 8 and y = −3x − 1?
Parallel. Both slopes are −3, and the y-intercepts (8 and −1) are different.
Card 7
Parallel, perpendicular or neither: y = 8x − 1 and y = −8x + 3?
Neither. The slopes are opposites, but the product is 8 × (−8) = −64, not −1.
Card 8
What is the slope of the line 3x + 4y = 8?
−3/4. Solve for y: 4y = −3x + 8, so y = −(3/4)x + 2. The slope is not 3.
Card 9
Write the line through (0, 6) that is parallel to y = −5x + 2.
y = −5x + 6. The slope stays −5, and the point (0, 6) has x = 0, so b = 6.
Card 10
Write the line through (4, 1) that is perpendicular to y = x/2 + 8.
y = −2x + 9. The slope 1/2 becomes −2. Then 1 = −2(4) + b, so b = 9.
Card 11
Two lines have the same slope and the same y-intercept. Are they parallel?
No. They are the same line. Parallel lines are two different lines that never meet.
Card 12
Are x = 4 and y = 10 parallel, perpendicular or neither?
Perpendicular. x = 4 is vertical and y = 10 is horizontal.
Card 13
Why can’t the flip-and-change-sign rule be used on a horizontal line?
Its slope is 0, and 0 has no reciprocal (1 ÷ 0 is undefined). The perpendicular partner of a horizontal line is a vertical line, which has an undefined slope.
Card 14
How do you check that a new line really passes through the given point?
Substitute the point’s x and y into your equation. Both sides must match.
Card 15
In this lesson’s SLIP memory trick, what do the letters stand for?
Slope of the given line, Look (same slope for parallel, flip and change sign for perpendicular), Insert the point into y = mx + b, Pull out b and write the equation.