Solved Examples and Worksheet for Using Graphs to represent Proportional Relationships

Q1A bus is traveling at an average speed of 100 miles per hour. Which of the graphs represents the distance travelled by the bus with respect to time?.

A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
d = 100 t
[Original equation.]
Step: 2
d = 100(0)
[Substitute 0 for t.]
Step: 3
= 0
[Simplify.]
Step: 4
d = 100(1)
[Substitute 1 for t.]
Step: 5
= 100
[Simplify.]
Step: 6
d = 100(2)
[Substitute 2 for t.]
Step: 7
= 200
[Simplify.]
Step: 8
d = 100(3)
[Substitute 3 for t]
Step: 9
= 300
[Simplify.]
Step: 10
Represent the above data in tabular form, as shown below.
Step: 11
Among the choices, graph-2 suits the result.
Correct Answer is :   Graph 2
Q2The graph shows relationship between cost of apples and its weight. If James buys 12 lbs of apples, how much will he pay?

A. 40
B. 44
C. 48
D. 43

Step: 1
In the graph, x-axis represents Weights of apples and y-axis represents the cost of apples.
Step: 2
From, the graph the cost of 12 lbs apples is $48. Step: 3 So, James has to pay$ 48 for 12 lbs of apples.
Q3Rosa had a pair of jeans that worth $8. Which graph shows the relationship between the number of jeans and the total cost? A. Graph 3 B. Graph 2 C. Graph 4 D. Graph 1 Step: 1 Cost of a pair of jeans =$8
Step: 2
Cost of n pairs of Jeans= $8× n Step: 3 The following table shows the total cost for the corresponding number of pairs of Jeans. Step: 4 The points plotted in Graph 1 are same as the values obtained in the table. Step: 5 Graph 1 shows the relationship between the number of pairs of Jeans and the total cost. Correct Answer is : Graph 1 Q4Ron bought a pen for$0.50. Which graph shows the relationship between the number of pens bought and the total cost?

A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Step: 1
Cost of a Pen= $0.50 Step: 2 Cost of n Pens =$0.50× n
Step: 3
The following table shows the total cost for the corresponding number of Pens.
Step: 4
The points plotted in Graph 4 are same as the values obtained in the table.
Step: 5
Graph 4 shows the relationship between the number of pens and the total cost.
Correct Answer is :   Graph 4
Q5Tim bought 2 boxes of crayons for $1.5. Which graph shows the relationship between the number of boxes of crayons bought and the total cost? A. Graph 4 B. Graph 3 C. Graph 1 D. Graph 2 Step: 1 Cost of 2 boxes of Crayons =$1.5
Step: 2
The following table shows the total cost for the corresponding number of boxes of Crayons.
Step: 3
The points plotted in Graph 3 are same as the values obtained in the table.
Step: 4
Graph 3 shows the relationship between the number of boxes of crayons and the total cost.
Correct Answer is :   Graph 3
Q6Identify a graph that shows the relationship between the number of feet and the number of inches.

A. Graph 4
B. Graph 2
C. Graph 3
D. Graph 1

Step: 1
1 foot = 12 inches
Step: 2
Make a table of values for this relation.
Step: 3
Plot the values on a coordinate plane and join the points.
Step: 4
The graph looks like the one below.
Step: 5
So, Graph 1 shows the relation between the number of feet and the number of inches.
Correct Answer is :   Graph 1
Q7A machine can make 1,500 bolts in 3 hours. Which graph shows the relationship between the number of bolts produced by the machine and the time taken?

A. Graph 2
B. Graph 4
C. Graph 1
D. Graph 3

Step: 1
The number of bolts produced by the machine in 1 hour = 15003 = 500.
Step: 2
As the time goes on, the total number of bolts produced by the machine, increases.
Step: 3
The direct variation between the number of bolts produced by the machine and the time taken can be given as, number of bolts produced in x hours is 500 × x.
Step: 4
The number of bolts produced and the time taken is shown in the table.
Step: 5
Graph 4 shows the relationship between the number of bolts produced by the machine and time taken.
Correct Answer is :   Graph 4
Q8Identify the graph that shows the relation between the number of workers and the time taken (days) by them to finish a particular job.

A. Graph 1
B. Graph 3
C. Graph 2
D. Graph 4

Step: 1
As the number of workers increase, the time taken by them to finish the job decreases.
Step: 2
Inverse variation is a relationship between two variables, in which, the product is a constant. When one variable increases the other decreases in proportion, so that the product is unchanged.
Step: 3
Therefore, Graph 4 shows the relation between the number of workers and the time taken by them to finish a particular job.
Correct Answer is :   Graph 4
Q9The graph shows the relationship between the cost and the number of chocolates. If Laura wants to buy 16 chocolates, how much does she need to pay?

A. $6 B.$4
C. $3 D.$5

Step: 1
In the graph, the x-axis represents the number of chocolates and the y-axis represents its cost.
Step: 2
From the graph, cost of 16 chocolates is $4. Step: 3 So, Laura has to pay$4 to buy 16 chocolates.
Correct Answer is :   $4 Q10The graph shows the relationship between the number of words Jim typed and the time taken to type. How many words did he type in 7 minutes ? A. 240 words B. 180 words C. 150 words D. 210 words Step: 1 In the graph, the x-axis represents the number of minutes and the y-axis represents the number of words typed. Step: 2 From the graph, the number of words typed in 7 minutes is 210. Step: 3 So, Jim typed 210 words in 7 minutes. Correct Answer is : 210 words Q11Identify the graph that best represents the relationship between the volume of a sphere and its radius r. [Take π = 3] A. Graph 1 B. Graph 2 C. Graph 3 D. Graph 4 Step: 1 Volume of a sphere V = 43πr3 Step: 2 Make a table of values for the volume V = 43πr3.  r 43 πr3 V (r, V) 1 43 (3)(1)3 4 (1, 4) 2 43 (3)(2)3 32 (2, 32) 3 43 (3)(3)3 108 (3, 108) 4 43 (3)(4)3 256 (4, 256) Step: 3 Graph the ordered pairs as shown. Step: 4 Graph 4 matches the above graph. Step: 5 So, Graph 4 best represents for the volume of a sphere with radius r. Correct Answer is : Graph 4 Q12A worker earns$25 per hour in a company. Which graph shows the relationship between the number of hours and the amount earned?

A. Graph 4
B. Graph 2
C. Graph 3
D. Graph 1

Step: 1
Let a, t represent the amount earned and the time respectively.
Step: 2
a = 25t
[Original equation.]
Step: 3
At t = 1, a = 25(1) = 25
Step: 4
At t = 2, a = 25(2) = 50
Step: 5
At t = 3, a = 25(3) = 75
Step: 6
At t = 4, a = 25(4) = 100
Step: 7
At t = 5, a = 25(5) = 125
Step: 8
Represent the above data in tabular form, as shown below.
 Input (t) 1 2 3 4 5 Output (a) 25 50 75 100 125
Step: 9
Among the choices, Graph 1 suits the result.
Correct Answer is :   Graph 1
Q13Kevin bought a hotdog for \$3. Which graph shows the relationship between the number of hotdogs bought and the total cost?

A. Graph 4
B. Graph 3
C. Graph 1
D. Graph 2

Step: 1
Let n, c represent the number of hotdogs bought and the total cost respectively.
Step: 2
c = 3n
[Original equation.]
Step: 3
At n = 1, c = 3(1) = 3
Step: 4
At n = 2, c = 3(2) = 6
Step: 5
At n = 3, c = 3(3) = 9
Step: 6
At n = 5, c = 3(5) = 15
Step: 7
At n = 4, c = 3(4) = 12
Step: 8
Represent the above data in tabular form, as shown below.
 Input (n) 1 2 3 4 5 Output (c) 3 6 9 12 15
Step: 9
Among the choices, Graph 3 suits the result.
Correct Answer is :   Graph 3
Q14A pipe can discharge 6 liters of water in 3 minutes. The graph shows the relationship between the number of minutes and the amount of water discharged. How long will it take to discharge 16 liters of water?

A. 18 minutes
B. 32 minutes
C. 8 minutes
D. 16 minutes

Step: 1
Locate 16 on the vertical axis. Follow the horizontal line through 16 till the line meets the graph at P (say). From P take a vertical line to meet the horizontal axis. This meeting point gives the time it takes to discharge 16 liters of water i.e. 8 minutes..
Correct Answer is :   8 minutes