2-2: Linear Equations: y = mx

Part 1

Example Writing Linear Equations from Graphs

The graph shows the distance d a car travels in time t at a constant speed r.

  • a. What is the constant speed of the car?

  • b. How far will the car travel in 2 h?

  • c. How long will it take the car to travel 120 mi?

  • d. Write an equation in d = rt form to model the situation shown.

A graph.

Solution

  • a. The car is traveling at a constant speed r of 30 mi/h.

  • b. The car will travel 60 mi in 2 h.

  • c. It will take 4 h to travel 120 mi.

  • d. The equation d = 30t models this situation.

(1, 30) = 30 mi/h. (2, 60) = 60 mi in 2 h. (4, 120) = 120 mi in 4 h.

Key Concept

Recall that the graph of a proportional relationship is a line that passes through the origin. An equation that models a proportional relationship can be written in the form y = mx. The equation y = mx shows y is always a constant multiple m of x.

An equation in the form y = mx is an example of a linear equation.

An equation is a linear equation if the graph of all of its solutions is a line.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties