Slope as Rate of Change

Learn slope from two points, horizontal and vertical lines.

Lesson 1 of 32 parts Practice Flashcards

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Slope from Two Points

Objective: Explain slope from two points, apply the stated method, and check its conditions.

Slope is (y₂−y₁)/(x₂−x₁) for distinct x-coordinates. It measures signed vertical change per horizontal change. The point order must match in numerator and denominator; a vertical line has undefined slope because its horizontal change is zero. A vertical line has undefined slope, not zero slope.

Formulas

$m=Δy/Δx, Δx≠0$

Worked examples

Try itFind slope through (7,7) and (13,49).Show answer

Step 1: Use m=(y₂−y₁)/(x₂−x₁). Step 2: The changes are 42 and 6. Step 3: m=7.

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Slope from Two Points

Objective: Explain slope from two points, apply the stated method, and check its conditions.

Formulas

$m=Δy/Δx, Δx≠0$

Worked examples

Try itFind slope through (7,7) and (13,49).Show answer

Step 1: Use m=(y₂−y₁)/(x₂−x₁). Step 2: The changes are 42 and 6. Step 3: m=7.

Horizontal and Vertical Lines

Objective: Explain horizontal and vertical lines, apply the stated method, and check its conditions.

A horizontal line has constant y and zero slope when two distinct x-values are compared. A vertical line has constant x and undefined slope. Zero and undefined are different: only the latter would require division by zero. Zero slope and undefined slope describe different orientations.

Formulas

Horizontal: y=k; vertical: x=h

Worked examples

Try itFind slope through (6,7) and (13,7).Show answer

Step 1: The vertical change is zero. Step 2: The horizontal change is 7, not zero. Step 3: Slope is 0/7=0.

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