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A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. They sold each ticket for
$45.
Let
y represent the net profit (in dollars) when they have sold
x tickets.
Which of the following information about the graph of the relationship is given?
Choose 1 answer:
(A) Slope and
x-intercept
(B) Slope and
y-intercept
(c) Slope and a point that is not an intercept
(D)
x-intercept and
y intercept
(E)
y-intercept and a point that is not an intercept
(F) Two points that are not intercepts

A charity organization had to sell $18$ tickets to their fundraiser just to cover necessary production costs. They sold each ticket for $\$45$ . Let $y$ represent the net profit (in dollars) when they have sold $x$ tickets. Which of the following information about the graph of the relationship is given? $\newline$ Choose $1$ answer: $\newline$ (A) Slope and $x$ -intercept $\newline$ (B) Slope and $y$ -intercept $\newline$ (C) Slope and a point that is not an intercept $\newline$ (D) $x$ -intercept and $y$ intercept $\newline$ (E) $y$ -intercept and a point that is not an intercept $\newline$ (F) Two points that are not intercepts

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Interpret the slope and y-intercept of a linear function

Full solution

Q. A charity organization had to sell

18

tickets to their fundraiser just to cover necessary production costs. They sold each ticket for

\$45

. Let

y

represent the net profit (in dollars) when they have sold

x

tickets. Which of the following information about the graph of the relationship is given?

\newline

Choose

1

answer:

\newline

(A) Slope and

x

-intercept

\newline

(B) Slope and

y

-intercept

\newline

(C) Slope and a point that is not an intercept

\newline

(D)

x

-intercept and

y

intercept

\newline

(E)

y

-intercept and a point that is not an intercept

\newline

(F) Two points that are not intercepts

Understand Relationship: Understand the relationship between the number of tickets sold and the net profit. The net profit $y$ is determined by the number of tickets sold $x$ minus the production costs. The production costs are covered by selling the first $18$ tickets, which means that the net profit starts at $\$0$ when $18$ tickets are sold.
Determine Slope: Determine the slope of the relationship. $\newline$ The slope represents the rate of change of the net profit with respect to the number of tickets sold. Since each ticket is sold for $\$45$ , the slope is $\$45$ per ticket.
Determine Y-Intercept: Determine the y-intercept of the relationship. $\newline$ The y-intercept is the net profit when no tickets are sold. Since the organization needs to sell $18$ tickets to cover production costs, the y-intercept is the negative value of the production costs. To find this, we multiply the number of tickets needed to cover costs ( $18$ ) by the price per ticket ( $\$45$ ), which gives us a y-intercept of $-18 \times \$45 = -\$810$ .
Determine X-Intercept: Determine the x-intercept of the relationship. $\newline$ The x-intercept is the number of tickets sold when the net profit is $\$0$ . We already know that they need to sell $18$ tickets to break even, so the x-intercept is $18$ .
Identify Given Information: Identify the given information based on the graph. $\newline$ We have determined both the slope ( $45 per ticket) and the x-intercept ($ $18$ tickets). Therefore, the information given about the graph of the relationship is the slope and the x-intercept.

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