Applications of Graphs
The coordinates of a point may represent something other than a location in the two dimensions. For instance, the first coordinate might represent the year and the second coordinate might represent the number of units sold by a business during that year. So, the point (1992,300,000) would tell you that the business sold 300,000 units during the year 1992. Or in another case the first coordinate might be your average speed on a trip and the second coordinate might be your gasoline mileage. Here, the point (68,29) would convey the information that when you averaged 68 mph on a trip, your gasoline mileage was 29 mpg.
Sometimes in cases like this, one or both of the axes are drawn with only positive numbers on them since none of the quantities considered could be negative. In other words, the graph will often lie entirely in the first quadrant.
Example 28. Suppose your gasoline mileage is represented by y and your average speed is represented by x. If y = 35 - 0.1x gives the relationship between your gasoline mileage and your average speed for speeds of 30 miles per hour or more, find your gasoline mileage when you average 60 miles per hour.
Answer:
Replacing x with 60 yields y = 35 - 0.1(60) or y = 29 mpg. Your gasoline mileage will be 29 miles per gallon when you average 60 miles per hour.
Example 29. Graph the relationship in the previous example.
Answer:
Since we know that the equation is only true for speeds of 30 mph and above, we find the value of y when x is 30. We get y = 35 - 0.1(30) = 35 - 3 = 32. This corresponds to the point (30,32). From the previous example we have the point (60,29). Then graph the two points as shown below and connect them with a line. The points are circled on the graph.
