A charity organization had to sell tickets to their fundraiser just to cover necessary production costs. They sold each ticket for $. Let$ represent the net profit (in dollars) when they have sold $ tickets. Which of the following information about the graph of the relationship is given? Choose $1$ answer: Choose $1$ answer:$\newline$(Choice A) Slope and $y$-intercept A Slope and $y$-intercept$\newline$(Choice B) Slope and $y$-intercept B Slope and $y$-intercept$\newline$(Choice C) Slope and a point that is not an intercept C Slope and a point that is not an intercept$\newline$(Choice D) $x$-intercept and $y$-intercept D $x$-intercept and $y$-intercept$\newline$(Choice E) $x$-intercept and a point that is not an intercept E $x$-intercept and a point that is not an intercept$\newline$(Choice F) Two points that are not intercepts F Two points that are not intercepts$\newline$Report a problem $2$ of $16$

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Grade 8

Write a linear equation from a slope and y-intercept

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Q. A charity organization had to sell tickets to their fundraiser just to cover necessary production costs. They sold each ticket for

. Let

represent the net profit (in dollars) when they have sold $ tickets. Which of the following information about the graph of the relationship is given? Choose $1$ answer: Choose $1$ answer:$\newline$(Choice A) Slope and $y$-intercept A Slope and $y$-intercept$\newline$(Choice B) Slope and $y$-intercept B Slope and $y$-intercept$\newline$(Choice C) Slope and a point that is not an intercept C Slope and a point that is not an intercept$\newline$(Choice D) $x$-intercept and $y$-intercept D $x$-intercept and $y$-intercept$\newline$(Choice E) $x$-intercept and a point that is not an intercept E $x$-intercept and a point that is not an intercept$\newline$(Choice F) Two points that are not intercepts F Two points that are not intercepts$\newline$Report a problem $2$ of $16$

Identify variables and relationship: Identify the variables and the relationship between them. $\newline$ In this problem, we are dealing with a charity organization that sells tickets to cover production costs and make a profit. The net profit (let's call it $P$ ) depends on the number of tickets sold (let's call it $T$ ). The relationship between $P$ and $T$ is linear, and we can express it as $P = mT + b$ , where $m$ is the slope (the amount of profit per ticket) and $b$ is the y-intercept (the initial profit or loss before any tickets are sold).
Determine missing values: Determine the missing values in the problem statement. $\newline$ The problem statement seems to be missing specific numerical values for the slope, $y$ -intercept, and the number of tickets that need to be sold to cover production costs. Without these values, we cannot determine the exact slope or $y$ -intercept.
Analyze given choices: Analyze the given choices to understand what information they are asking for. $\newline$ (Choice A) Slope and $y$ -intercept $\newline$ (Choice B) Slope and $x$ -intercept $\newline$ (Choice C) Slope and a point that is not an intercept $\newline$ (Choice D) $y$ -intercept and $x$ -intercept $\newline$ (Choice E) $y$ -intercept and a point that is not an intercept $\newline$ (Choice F) Two points that are not intercepts $\newline$ We need to figure out which of these choices can be determined from the information given in the problem statement.
Assess provided information: Assess the information provided in the problem statement. $\newline$ The problem statement does not provide any specific numerical values, but it does mention that the net profit $P$ is related to the number of tickets sold $T$ . Since we do not have any specific values, we cannot determine the slope or intercepts directly. However, we know that the slope represents the rate at which profit changes with the number of tickets sold, and the $y$ -intercept would represent the initial profit or loss before any tickets are sold.
Conclude correct choice: Conclude which choice is correct based on the information given. $\newline$ Since the problem statement does not provide any specific numerical values for the slope or intercepts, we cannot choose any of the options that require specific numerical information (Choices A, B, D, E, F). The only choice that does not require specific numerical values is Choice C, which states ＂Slope and a point that is not an intercept.＂ This choice is the most appropriate because we know the relationship is linear (implying a slope), and we know that there is a point where the net profit is zero (the break-even point), which is not an intercept since it's not given as the $y$ -intercept.