A proportional relationship between two quantities is the one in which the rate of change is constant or one in which the ratio of one quantity to the other is constant.
In this section, we are going to see, how proportional relationships can be graphed. A relationship is a proportional relationship if its graph is a straight line.
Example 1 :
The equation y = 5x represents the relationship between the number of gallons of water used (y) and the number of minutes (x) for most shower heads manufactured before 1994. Graph the above relationship and check whether it is proportional.
Solution :
Step 1 :
To graph the given relationship, let us plug some random values for x in y = 5x as given in the table.
Step 2 :
Write the data in the table as ordered pairs (time, water used).
(1, 5), (2, 10), (3, 15), (7, 35) and (10, 50)
Step 3 :
Plot the ordered pairs and connect all the points.
Step 4 :
Because the line drawn through the points goes through the origin, the relationship is proportional.
Example 2 :
The table shows the relationship between the amount charged by a housecleaning company ($) and the amount of time worked (hours). Is the relationship a proportional relationship? Explain.
Solution :
Step 1 :
Write the data in the table as ordered pairs (time, water used).
(1, 5), (2, 10), (3, 15), (7, 35) and (10, 50)
Step 2 :
Plot the ordered pairs and connect all the points.
Step 3 :
Because the line drawn through the points goes through the origin, the relationship is proportional.
Example 3 :
Jared rents bowling shoes for $6 and pays $5 per bowling game. Is the relationship a proportional relationship? Explain.
Solution :
Step 1 :
Write the data in the table as ordered pairs (time, water used).
(1, 11), (2, 16), (3, 21), and (4, 26)
Step 2 :
Plot the ordered pairs and connect all the points.
Step 3 :
Because the line drawn through the points does not go through the origin, the relationship is not proportional.
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