Rate of Change and Slope

Learn and apply rate of change and slope using equations, examples, and interpretation.

Lesson 1 of 53 parts Practice Flashcards

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Rise Over Run

Objective: Explain and use rise over run in an Algebra 1 problem.

Slope m=(y₂−y₁)/(x₂−x₁) measures vertical change per unit horizontal change when x₂≠x₁. A zero horizontal change between distinct points.

Worked examples

Try itExample 1.1: Find the slope through (0,14) and (5,34).Show answer

4. Divide the change in y by the change in x. The answer is 4.

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Rise Over Run

Objective: Explain and use rise over run in an Algebra 1 problem.

Slope m=(y₂−y₁)/(x₂−x₁) measures vertical change per unit horizontal change when x₂≠x₁. A zero horizontal change between distinct points.

Worked examples

Try itExample 1.1: Find the slope through (0,14) and (5,34).Show answer

4. Divide the change in y by the change in x. The answer is 4.

Positive and Negative Slopes

Objective: Explain and use positive and negative slopes in an Algebra 1 problem.

A positive slope rises as x increases, a negative slope falls, and a horizontal line has slope zero. No, its slope is zero.

Worked examples

Try itExample 2.1: Find the slope through (0,24) and (8,40).Show answer

2. Divide the change in y by the change in x. The answer is 2.

Units of Slope

Objective: Explain and use units of slope in an Algebra 1 problem.

Slope units are output units divided by input units; in a distance-time graph they may be kilometers per hour. A bare number may hide what changes per what.

Worked examples

Try itExample 3.1: Find the slope through (0,34) and (11,67).Show answer

3. Divide the change in y by the change in x. The answer is 3.

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