# Graph Linear Functions Worksheet - Page 11

Graph Linear Functions Worksheet
• Page 11
101.
Mr. Chris requires $x$ gallons of milk for their family. The cost of $x$ gallons of milk is given by $f$($x$) = 1.19$x$. Which of the tables best suits the equation?

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

#### Solution:

f(x) = 1.19x
[Original equation.]

f(1)= 1.19(1) = 1.19
[Substitute 1 for x and simplify.]

f(2) = 1.19(2) = 2.38
[Substitute 2 for x and simplify.]

f(3) = 1.19(3) = 3.57
[Substitute 3 for x and simplify.]

f(4)= 1.19(4) = 4.76
[Substitute 4 for x and simplify.]

Table 3 matches with the equation.

102.
Find the slope and $y$-intercept of the function $f$($x$) = 9.1 + 0.25$x$.
 a. Slope = 9.35, $y$-intercept = 0.50 b. Slope = 0.25, $y$-intercept = 9.1 c. Slope = 9.1, $y$-intercept = 0.25 d. Slope = 0.50, $y$-intercept = 9.35

#### Solution:

f(x)= 0.25x + 9.1
[Original equation.]

f(x) = mx + c
[Standard equation.]

The slope of the function m is 0.25 and the y-intercept, c is 9.1.
[Compare with the standard equation.]

103.
If $f$($x$) = 0.95$x$ + 2.3, then find the value of $f$(2) and $f$(3).
 a. 5.20, 6.65 b. 4.20, 5.15 c. 3.70, 5.65 d. 5.35, 7.30

#### Solution:

f(x) = 0.95x + 2.3
[Original equation.]

f(2) = 0.95(2) + 2.3
[Substitute 2 for x.]

= 4.20
[Simplify.]

f(3) = 0.95 (3) + 2.3
[Substitute 3 for x.]

= 5.15
[Simplify.]

So, f(2) = 4.20 and f(3) = 5.15

104.
Marissa and Jessica wanted to organize a farewell party for their seniors. They collected an amount of $800 from the class. The caterers charged$50 for each person. Which of the following functions shows the amount left with them?
 a. $f$($x$) = 850 + 800$x$ b. $f$($x$) = 800 - 50$x$ c. $f$($x$) = 850 - 800$x$ d. None of the above

#### Solution:

The total amount collected from the class = $800. The amount charged by caterers per person =$50.

The balance depends on the number of people who attended the party = f(x) = 800 - 50x.

f(x) = 800 - 50x.
[Function rule.]

105.
Which of the input-output tables forms a linear function?

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

#### Solution:

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

In the first table change in f(x)change in x is not same through out. So, it is ruled out.

[Consider table2.]

The change in input (x) is 3 and the change in output f(x) is 4.

Change in f(x)Change in x = 4 / 3

Among the choices, table 2 forms a linear function.
[The ratio of the change in f(x) to the change in x is same throughout the table.]

106.
Find the linear function for the graph.

 a. $f$($x$) = ()$x$ + 10 b. $f$($x$) = ()$x$ +12 c. $f$($x$) = ()$x$ + 11 d. None of the above

#### Solution:

Represent the data in the graph in a table, as shown below.

The change in input, x is + 2 and the change in output, f(x) is - 3.

Change in f(x)Change in x = -3 / 2

So, the slope of the function is - 32 .

The point (0, 10) lies on the graph of the function. So, the y - intercept is 10.

The function rule which governs the graph is f(x) = - 32x + 10
[Write the linear function as f(x) = mx + c.]

107.
Fuel is being pumped into a tanker at a rate of 75 gallons per minute. The quantity of fuel in the tanker is a function of the number of minutes the fuel is pumped. Which of the following equations represents the quantity of fuel in the tanker?
 a. A = $\frac{75}{n}$ b. A= 75 - n c. A= 75 + $n$ d. A = 75$n$

#### Solution:

The rate at which fuel is being pumped is 75 gallons per minute.

Let n be the number of minutes, for which fuel is pumped and A be the amount of fuel in the tank.

The amount of fuel in the tank, A = 75 x number of minutes for which fuel is pumped

So, the equation representing the amount of fuel in the tanker is A = 75n

108.
A Painting exhibition is being organized in Milan. The painters who wish to exhibit and sell their paintings need to pay $100 for the space and$20 for each painting they sell. Which of the following equations best suits the function rule that represents the amount paid to the organizers as a function of number of paintings sold? Represent this as a function table showing input and output.
 a. $f$($x$) = 100 + 20$x$ b. $f$($x$) = 100 + 30$x$ c. $f$($x$) = 120 + 20$x$ d. None of the above

#### Solution:

Amount to be paid for space = $100. Amount to be paid for each painting =$20.

Input(x) = Number of paintings each painter sells.

Output f(x) = Amount paid by each painter.

f(x) = 100 + 20x.

109.
A fete is being organized in a school. Students need to pay $50 to put up a games stall and$2 on every ticket they sell for the game. How much should each stall owner pay? Express this as a function rule.
 a. f ($x$) = 50 - 2$x$ b. f ($x$) = 50 - $x$ c. f($x$) = 50 + 2$x$ d. f ($x$) = 50 + $x$

#### Solution:

Let x be the number of tickets sold by the games stall owner.
[Input.]

Let f(x) be the amount earned by the stall owner.
[Output.]

f(x) = 50 + 2x
[Function rule.]

An input-output table is drawn, for the corresponding input values x = 4, 6, 8 and 10.

110.
Which of the following function rules best suits the graph?

 a. $y$ = 4 + 2$x$ b. $y$ = 6 - 2$x$ c. $y$ = 7 + 3$x$ d. $y$ = - 5 + 3$x$

#### Solution:

Represent the data in the graph in a tabular form, as shown below.

The change in input (x) = 1

The change in output (y) = + 3

Change in yChange in x = + 31 = 3.

The slope of the line is 3 and y-intercept is - 5.
[Slope of the line is change in ychange in x.]

y = - 5 + 3x.
[Function rule.]