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Graph Linear Functions Worksheet - Page 7

Graph Linear Functions Worksheet
  • Page 7
 61.  
The graph shows how quickly a swimmer expends calories. Which equation best represents the data in the graph?


a.
Ct = 10
b.
C = 10t
c.
t = 10C
d.
C = 100t


Answer: (b)


Correct answer : (2)
 62.  
Which of the following equations is not a linear equation?
a.
25z = 29
b.
2 - 3x = 4x
c.
3x + 5 = 47x
d.
(x - 8)3 = 66


Solution:

An algebraic equation is said to be linear if the variable or variables in the equation are of first degree.

In the equation (x - 8)3 = 66, x is raised to the power 3.

So, (x - 8)3 = 66 is not a linear equation.


Correct answer : (4)
 63.  
Which of the following equations is not a linear equation?
a.
7x = 12x + 46
b.
x - 5x - 6 = 0
c.
x2 - 5x - 6 = 0
d.
7x = 121


Solution:

An algebraic equation is said to be linear if the variable or variables in the equation are of first degree.

In the equation x2 - 5x - 6 = 0, x is raised to the power 2.

So, x2 - 5x - 6 = 0 is not a linear equation.


Correct answer : (3)
 64.  
Which is a linear function?
a.
x + y - 7 = 0
b.
y2 = 4x
c.
4y - (21 x) = 1
d.
2xy - 1 = 0


Solution:

A linear function is of the form y = mx + b.

x + y - 7 = 0 gives y = 7 - x
[Keep 'y' on one side, bring the rest to the other side.]

4y - (21 / x) = 1 gives y = (21 / 4x) + 1 / 4

2xy - 1 = 0 gives y = 12x

y2 = 4x is not in the form y = mx + b

So, x + y - 7 = 0 represents a linear function.


Correct answer : (1)
 65.  
Identify the graph that represents a linear model.

a.
Graph 1
b.
Graph 3
c.
Graph 2
d.
Graph 4


Solution:

The graph of a linear model is a straight line

Graph 4 is a straight line.

So, Graph 4 represents a linear model.


Correct answer : (4)
 66.  
Identify the graph that represents a non-linear model.

a.
Graph 2
b.
Graph 4
c.
Graph 1
d.
Graph 3


Solution:

The graph of a linear model is a straight line.

Graphs 1, 2, and 3 are straight lines.

Therefore, Graphs 4 represents a non-linear model.


Correct answer : (2)
 67.  
Identify the table that represents a non-linear function.


a.
Table 2
b.
Table 1
c.
Table 3
d.
Table 4


Solution:

A table is said to be a non-linear function if the ratio of change in output to input is not same throughout the table.

In the tables 1, 2 and 4, change in f(x)change in x is same throughout.

In the table 3, change in f(x)change in x is not same throughout.

Therefore, Table 3 represents a non-linear function.


Correct answer : (3)
 68.  
A train is traveling at an average speed of 100 miles per hour. Which of the graphs represents the distance traveled by the train with respect to time?

a.
Graph 2
b.
Graph 3
c.
Graph 1
d.
Graph 4


Solution:

Let d, t represent the distance and time respectively.

d = 100t
[Original equation.]

At t = 0, d = 100(0) = 0

At t = 1, d = 100(1) = 100

At t = 2, d = 100(2) = 200

At t = 3, d = 100(3) = 300


Represent the above data in tabular form, as shown below.

Among the choices, Graph 2 suits the result.


Correct answer : (1)
 69.  
Steven bought a watch for $40. Which graph shows the relationship between the number of watches bought and the total cost?

a.
Graph 2
b.
Graph 4
c.
Graph 1
d.
Graph 3


Solution:

Let n, c represent the number of watches bought and the total cost.

c = 40n
[Original equation.]

At n = 1, c = 40(1) = 40

At n = 2, c = 40(2) = 80

At n = 3, c = 40(3) = 120

At n = 4, c = 40(4) = 160

At n = 5, c = 40(5) = 200

Represent the above data in tabular form, as shown below.
Input (n)12345
Output (c)4080120160200


Among the choices, Graph 2 suits the result.


Correct answer : (1)
 70.  
A worker earns $25 per hour in a company. Which graph shows the relationship between the number of hours and the amount earned?

a.
Graph 3
b.
Graph 1
c.
Graph 4
d.
Graph 2


Solution:

Let a, t represent the amount earned and the time respectively.

a = 25t
[Original equation.]

At t = 1, a = 25(1) = 25

At t = 2, a = 25(2) = 50

At t = 3, a = 25(3) = 75

At t = 4, a = 25(4) = 100

At t = 5, a = 25(5) = 125

Represent the above data in tabular form, as shown below.
Input (t)12345
Output (a)255075100125


Among the choices, Graph 1 suits the result.


Correct answer : (2)

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