Chapter 4.2, Problem 17PPE

To determine

The relationship between the amount of gas used and the distance traveled using a table, an equation, and a graph.

Whether total distance traveled is a function of the gas used.

The independent and dependent variables.

Explanation of Solution

Given information:

An automaker makes a car that can travel 40 mi on its charged battery before it begins to use gas. Then the car travels 50 mi per gallon of gas used.

Graph:

Distance that can be covered by a car on its charged battery $=40$ mi

Let $x$ denotes gas used.

Distance that can be covered by a car using 1 gallon of gas $=50$ mi

So,

Distance that can be covered by a car using $x$ gallons of gas $=50x$ mi

Therefore,

Total distance travelled by a car $=40+50x$ mi

Let $y$ denotes total distance travelled by car

So,

  $y=40+50x$

This is an equation.

Now draw the table.

At $x=0,y=40+50(0)=40$

At $x=1,y=40+50(1)=90$

At $x=2,y=40+50(2)=140$

At $x=3,y=40+50(3)=190$

x	0	1	2	3
y	40	90	140	190

Here, $y$ (total distance covered) is the dependent variable and $x$ (amount of gas used) is an independent variable as Total distance covered by car is depends on the amount of gas used.

Now draw the graph based on this table.

Plot the points $(0,40),(1,90),(2,140),(3,190)$ and join them