﻿ Graph Linear Functions Worksheet - Page 6 | Problems & Solutions

# Graph Linear Functions Worksheet - Page 6

Graph Linear Functions Worksheet
• Page 6
51.
Which of the following equations is not a linear equation?
 a. 2 + 3$x$ = 4 b. 3$x$ - 5 = 8$x$ c. ($x$ + 2)2 = 6 d. $x$ = 1

#### 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 + 2)2 = 6, x is raised to the power 2.

So, (x + 2)2 = 6 is not a linear equation.

52.
Identify a table that represents a linear function.

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

#### Solution:

A table is said to be a linear function if the ratio of change in output to input is same throughout the table.

In the tables 1, 2 and 4, change in f(x)change in x is not same throughout.

[Consider table 3.]

The change in input (x) is 1 and the change in output f(x) is 4.

change in f(x)change in x = 4 / 1

Among the choices, Table 3 forms a linear function.
[The ratio of the change in f(x) to the change in x is same throughout the table.]

53.
Identify the table that represents a non-linear function.

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

#### 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.

54.
Identify the graph that represents a linear function.

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

#### Solution:

The graph of a linear equation is a straight line.

Graph 4 is a straight line.

So, Graph 4 represents a linear equation.

55.
Which of the following situations best represents the graph?

 a. As the number of workers increase, time taken to finish the job decreases. b. As the time increases, amount of interest increases. c. As the number of pens increase, total cost increases. d. As the number of books increase, space occupied increases.

#### Solution:

From the graph, as the values on x-axis increase, the values on y-axis decrease.

Therefore, the situation that best represents the graph is 'As the number of workers increase, time taken to finish the job decreases.'

56.
Identify the graph that represents a linear model.

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

#### Solution:

The graph of a linear model is a straight line

Graph 4 is a straight line.

So, Graph 4 represents a linear equation.

57.
Identify the graph that represents a non-linear model.

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

#### 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.

58.
Which among the following is a linear function?
(i) 2$x$ + $y$ - 1 = 0
(ii) 2$y$ - ($\frac{10}{x}$) = 1
(iii) $\mathrm{xy}$ - 1 = 0
 a. only (i) b. only (ii) c. (i), (ii), and (iii) d. (i) and (ii)

#### Solution:

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

2x + y - 1 = 0 gives y = 1 - 2x
[Keep 'y' on one side, bring the rest to the other side.]

2y - (10 / x) = 1 gives y = (5 / x) + 1 / 2

xy - 1 = 0 gives y = 1x

Among the given equations, only 2x + y - 1 = 0 represents a linear function.

59.
Find the slope of the line in the graph.

 a. 2 b. $\frac{1}{2}$ c. - $\frac{1}{2}$ d. - 2

Find the $y$-intercept of the line 3$y$ - $x$ = 5.
 a. 5 b. - 5 c. $1\frac{2}{3}$ d. $\frac{1}{5}$