Write and graph an equation to represent the situation. You put 18 gallons of gasoline (x) in your car. You know that this amount of gasoline will allow you to drive 468 miles (y).
To write and graph an equation to represent the situation, we can use the concept of fuel efficiency, which is measured in miles per gallon (MPG).
The equation would take the form of y = mx + b, where:
- y is the number of miles driven,
- x is the number of gallons of gasoline used,
- m is the fuel efficiency in miles per gallon, and
- b is a constant representing any initial mileage your car may have.
In this case, the fuel efficiency m can be found by dividing the number of miles driven y by the number of gallons of gasoline used x.
So, m = y / x.
The equation becomes y = (y / x)x + b.
Simplifying this equation, we can rewrite it as y = (y / 18)x + b.
To graph this equation, let's assume b = 0 for simplicity. We can then plot a few points to plot a straight line on a graph:
- Let's take x = 0. In this case, y would be 0, since without any gasoline, you cannot drive any miles. So, the point (0, 0) is on the line.
- Let's take x = 18. In this case, y would be 468, since you know that 18 gallons of gasoline allows you to drive 468 miles. So, the point (18, 468) is on the line.
By connecting these two points with a straight line, we have the graph of the equation representing the situation.