Digits, Grade 7, Volume 1, Homework Helper

Topic 8: Representing Linear Relationships

8-1: Rate of Change

Key Concept

As you ride a bike up a hill, both your vertical distance (the rise) and your horizontal distance (the run) from the bottom of the hill change. You can measure the steepness of the hill by its slope, the ratio that compares the rise and run between two points on the hill.

The slope is also called the rate of change of the linear relationship that models the hill.

table with 2 rows and 2 columns , row1 column 1 , shop , column 2 equals . rateofchange . equals . fraction verticalchange , over horizontalchange end fraction , row2 column 1 , , column 2 equals . fraction rise , over run end fraction , end table

A line segment's right endpoint is higher than its left endpoint. An arrow labeled run extends from the left endpoint to a point directly below the right endpoint. Then another arrow labeled rise forms a right angle by extending up to the right endpoint of the segment.

The rate of change of a linear relationship is constant.

table with 2 rows and 2 columns , row1 column 1 , rateofchange , column 2 equals . fraction verticalchange , over horizontalchange end fraction , row2 column 1 , , column 2 equals , 6 eighths , comma or , 3 fourths , end table

A coordinate graph of a line passing through (0, 2) and (8, 8). A horizontal arrow extends 8 units from (0, 2) to the point directly below (8, 8). Then another arrow forms a right angle by extending up 6 units to (8, 8).


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Table of Contents

Digits, Grade 7, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Expressions, Equations, and Relationships Unit C: Measurement and Geometry Unit D: Proportionality English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties