Grade 10 — Mathematics 10C › C10U07 Linear Relations & Functions

Grade 10 › C10U07 Linear Relations & Functions › L4
GRADE 10 · ALBERTAOUTCOME RF3

L4 · Parallel and Perpendicular Slopes

Learning goal

“I can decide whether two lines are parallel, perpendicular, or neither by comparing their slopes, and find slopes and points for lines parallel or perpendicular to a given line.”

Parallel lines — lines in a plane that never meet; for non-vertical lines, they have EQUAL slopes.
Perpendicular lines — lines that meet at a right angle; their slopes are negative reciprocals (product -1).
Negative reciprocal — flip the fraction and change the sign: the negative reciprocal of 2/3 is -3/2; of -4 is 1/4. (Vertical and horizontal lines are the special perpendicular pair: undefined slope with slope 0.)
Worked example

Line A passes through (0, 2) and (2, 6): slope = (6 - 2) / (2 - 0) = 2. Line B passes through (0, -1) and (1, 1): slope = (1 - (-1)) / (1 - 0) = 2. The slopes are equal, so the lines climb identically and never meet - they are parallel. (Same slope but different starting points: if two lines had the same slope AND a shared point, they would be the same line, not two parallels.)

Check yourself — explain it

Parallel lines must have equal slopes because...

Paired problem — example still visible

Line C has slope -3/2. A line through (0, 5) with slope -3/2 - parallel to C or not? -> Parallel - the slopes are equal (-3/2).

Faded completion — last step is yours

"A line parallel to a line with slope 5 has slope ___." -> 5

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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