When two quantities x and y are proportional, the relationship can be represented by the equation y=mx.
B
Write the linear equation that represents the distance traveled by a car.
A
The car, see solution.
B
56 miles
Practice makes perfect
We are given an equation that represents the distance y in miles that a truck travels on x gallons of gasoline.
y=18x
The given graph shows the distance that a car travels.
We want to find which vehicle gets better gas mileage. To do so, remember that the slope is a ratio used to compare how a variable changes in relation to another variable.
m= Change iny/Change in x
In our case, the slope will tell us the distance traveled per gallons of gasoline. Then, to find the vehicle with better gas mileage we can calculate the slope of each case and see which one is greater. Notice that the equation of the truck is a proportional relationship.
y=mx
Here, m is the constant of proportionality. The graph of this equation is a line with a slope m that passes through the origin. The slope of the truck's gas mileage is equal to 18. Now, we will use the Slope Formula to calculate the slope of car. Let's use two points of the given graph!
The slope of the car is equal to 25. Since 25 is greater than 18, the car has better mileage than the truck.
We want to find how much farther the car can travel on 8 gallons of gasoline than the truck. To do so, remember that the graph of a proportional relationship is a line with a slope m that passes through the origin. Notice that the given graph of the car is a line passing through the origin.
This means that we can write the equation of the line as y=mx. To do so, recall that the slope of the line showing the distance traveled by a car is equal to m=25.
y=25x
Now, we will substitute x= 8 into the above equation to find the distance traveled.
