Slopes of Lines

Calculate and compare slope from points and graphs.

Lesson 4 of 53 parts Practice Flashcards

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Calculating Slope

Objective: Compute rise over run from two distinct points.

For (x₁,y₁),(x₂,y₂), slope m=(y₂−y₁)/(x₂−x₁) when x₂≠x₁. A vertical line has undefined slope.

A line through (1, 1) and (7, 5) with a run of 6 and rise of 4, so the slope is 2/3.

Formulas

$m=(y_2-y_1)/(x_2-x_1)$

Worked examples

Try itFind the slope through (1,2) and (4,8).Show answer

(8−2)/(4−1)=2.

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Calculating Slope

Objective: Compute rise over run from two distinct points.

For (x₁,y₁),(x₂,y₂), slope m=(y₂−y₁)/(x₂−x₁) when x₂≠x₁. A vertical line has undefined slope.

Formulas

$m=(y_2-y_1)/(x_2-x_1)$

Worked examples

Try itFind the slope through (1,2) and (4,8).Show answer

(8−2)/(4−1)=2.

Positive, Negative, Zero, Undefined

Objective: Classify slope and avoid division by zero.

A line rising left to right has positive slope; falling has negative slope; horizontal has zero slope; vertical has undefined slope.

Panels showing a rising line with positive slope, a falling line with negative slope, a horizontal zero slope and a vertical undefined slope.

Slope Tests for Line Relationships

Objective: Use slope to recognize parallel and perpendicular nonvertical lines.

Distinct nonvertical parallel lines have equal slopes. Perpendicular nonvertical lines have slopes with product −1. Horizontal and vertical lines are perpendicular.

Two teal parallel lines with slope one half and a red line of slope negative two meeting one of them at a right angle.

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