﻿ Graph Linear Functions Worksheet - Page 4 | Problems & Solutions

# Graph Linear Functions Worksheet - Page 4

Graph Linear Functions Worksheet
• Page 4
31.
Identify the graph that represents a linear function.

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

32.
Which table best suits the equation $y$ = $x$ + 16?

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

#### Solution:

y = x + 16
[Original equation.]

y = 2 + 16 = 18
[Substitute x = 2 and add.]

y = 4 + 16 = 20
[Substitute x = 4 and add.]

y = 6 + 16 = 22
[Substitute x = 6 and add.]

y = 7 + 16 = 23
[Substitute x = 7 and add.]

Table 1 matches the values.

So, Table 1 best suits the equation y = x + 16.

33.
Identify the table that suits the equation $y$ = 3$x$ + 2.

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

#### Solution:

y = 3x + 2
[Original equation.]

y = (3 × - 1) + 2 = - 1
[Substitute x = - 1 and simplify.]

y = (3 × 0) + 2 = 2
[Substitute x = 0 and simplify.]

y = (3 × 1) + 2 = 5
[Substitute x = 1 and simplify.]

y = (3 × 2) + 2 = 8
[Substitute x = 2 and simplify.]

Table 2 matches the values.

So, Table 2 best suits the equation y = 3x + 2.

34.
Which table best matches the equation $y$ = 5$x$?

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

#### Solution:

y = 5x
[Original equation.]

y = 5 × (- 2) = - 10
[Substitute x = - 2 and multiply.]

y = 5 × (- 1) = - 5
[Substitute x = - 1 and multiply.]

y = 5 × 0 = 0
[Substitute x = 0 and multiply.]

y = 5 × 1 = 5
[Substitute x = 1 and multiply.]

y = 5 × 2 = 10
[Substitute x = 2 and multiply.]

Table 1 matches the values.

So, among the given tables, Table 1 best matches the equation y = 5x.

35.
Identify the table that fits the equation $y$ = $x$ - 4.

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

#### Solution:

y = x - 4
[Original equation.]

y = 1 - 4 = - 3
[Substitute x = 1 and subtract.]

y = 2 - 4 = - 2
[Substitute x = 2 and subtract.]

y = 3 - 4 = - 1
[Substitute x = 3 and subtract.]

y = 4 - 4 = 0
[Substitute x = 4 and subtract.]

y = 6 - 4 = 2
[Substitute x = 6 and subtract.]

Table 4 matches with the values.

So, among the given tables, Table 4 fits the equation y = x - 4.

36.
Identify the table that matches the equation $y$ = 2$x$ + 3.

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

#### Solution:

y = 2x + 3
[Original equation.]

y = 2(0) + 3 = 3
[Substitute x = 0 and simplify.]

y = 2(1) + 3 = 5
[Substitute x = 1 and simplify.]

y = 2(2) + 3 = 7
[Substitute x = 2 and simplify.]

y = 2(3) + 3 = 9
[Substitute x = 3 and simplify.]

y = 2(4) + 3 = 11
[Substitute x = 4 and simplify.]

Table 2 matches with the values.

So, among the given tables, Table 2 matches the equation y = 2x + 3.

37.
Which rule describes the relationship between the input and output in the table shown?
 Input Output 4 7 5 8 6 9 7 10 8 11

 a. Output = Input + 3 b. Output = $\frac{Input}{3}$ c. Output = Input d. Output = Input - 3

#### Solution:

On observing the table it is found that the output 7 = 4 + 3, 8 = 5 + 3, 9 = 6 + 3, 10 = 7 + 3, and 11 = 8 + 3.

So, we can write the relationship between input and output as a rule, Output = Input + 3.

38.
Which of the following equations is true for the four pairs of $x$ and $y$ values shown in the table?
 $x$ - 2 - 5 0 1 $y$ 6 3 8 9

 a. $y$ = - $x$ - 8 b. $y$ = $x$ + 8 c. $y$ = 3$x$ + 3 d. $y$ = 2$x$ + 4

#### Solution:

On observing the table, it is found that 6 = - 2 + 8, 3 = - 5 + 8, 8 = 0 + 8, 9 = 1 + 8

So, the equation that best represents the relationship is, y = x + 8.

39.
Which of the equations best represents the rule for the table?
 $x$ 2 3 4 5 $y$ 10 15 20 25

 a. $y$ = 8$x$ + 5 b. $y$ = $x$ + 5 c. $y$ = 2$x$ + 5 d. $y$ = 5$x$

#### Solution:

On observing the table, it is found that 10 = 2 × 5, 15 = 3 × 5, 20 = 4 × 5, 25 = 5 × 5

So, the equation that best represents the rule for the table is y = 5x.

40.
Identify a equation that represents the rule for the pattern shown in the table.
 $x$ 4 6 8 10 $y$ 22 24 26 28

 a. $y$ = $x$ + 18 b. $y$ = 3$x$ + 6 c. $y$ = 4$x$ d. $y$ = 18$x$

#### Solution:

On observing the table, it is found that 22 = 4 + 18, 24 = 6 + 18, 26 = 8 + 18, 28 = 10 + 18

So, the equation that represents the rule for the pattern shown in the table is y = x + 18.