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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 $\$ 45$ . $\newline$ Let $y$ represent the net profit (in dollars) when they have sold $x$ tickets. $\newline$ 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

.

\newline

Let

y

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

x

tickets.

\newline

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

Calculate Fixed Costs: Determine the fixed costs and the variable profit per ticket. The charity organization needs to sell $18$ tickets at $\$45$ each to cover the production costs. This means the fixed costs are $18$ tickets * $\$45$ per ticket = $\$810$ .
Write Net Profit Equation: Write the equation for net profit $y$ in terms of the number of tickets sold $x$ . The net profit is calculated by subtracting the fixed costs from the total revenue. The total revenue is $\$45$ times the number of tickets sold $x$ . So, the equation is $y = 45x - 810$ .
Identify Slope: Identify the slope of the equation. $\newline$ The slope of the equation is the coefficient of $x$ , which is $45$ . This represents the additional profit for each additional ticket sold.
Identify Y-Intercept: Identify the y-intercept of the equation. $\newline$ The y-intercept is the point where the line crosses the y-axis, which occurs when $x = 0$ . In this equation, when $x = 0$ , $y = -810$ . This is the point $(0, -810)$ , which represents the net loss if no tickets are sold.
Determine X-Intercept: Determine if there is an x-intercept. The x-intercept occurs when $y = 0$ . To find the x-intercept, set the net profit to zero and solve for $x$ : $0 = 45x - 810$ . Solving for $x$ gives $x = \frac{810}{45} = 18$ . This is the point $(18, 0)$ , which represents the break-even point where the number of tickets sold covers the production costs.
Choose Correct Answer: Choose the correct answer based on the information given. $\newline$ We have determined both the slope of the line ( $45$ ) and the y-intercept ( $-810$ ). Therefore, the correct answer is (B) Slope and y-intercept.

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