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.
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.
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.