﻿ Graph Linear Functions Worksheet - Page 7 | Problems & Solutions

# 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. C$t$ = 10 b. C = 10$t$ c. $t$ = 10C d. C = 100$t$

62.
Which of the following equations is not a linear equation?
 a. 25$z$ = 29 b. 2 - 3$x$ = 4$x$ c. 3$x$ + 5 = 47$x$ 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.

63.
Which of the following equations is not a linear equation?
 a. 7$x$ = 12$x$ + 46 b. $x$ - 5$x$ - 6 = 0 c. $x$2 - 5$x$ - 6 = 0 d. 7$x$ = 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.

64.
Which is a linear function?
 a. $x$ + $y$ - 7 = 0 b. $y$2 = 4$x$ c. 4$y$ - ($\frac{21}{x}$) = 1 d. 2$x$$y$ - 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.

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.

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.

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.

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.

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) 1 2 3 4 5 Output (c) 40 80 120 160 200 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) 1 2 3 4 5 Output (a) 25 50 75 100 125

Among the choices, Graph 1 suits the result.