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A line graphed in the first quadrant of a coordinate plane shows number of campers versus total cost in dollars.

Quinn’s family is going camping. To get into a camping site, his family must pay a one-time parking fee and purchase a ticket for each family member. The graph shows the total cost Quinn’s family must pay to enter. Which of the following points can be used to find the linear equation that models this graph?

(1 point)
Responses

(3,45)
and (5,60)
left parenthesis 3 comma 45 right parenthesis and left parenthesis 5 comma 60 right parenthesis

(0,25)
and (2,40)
left parenthesis 0 comma 25 right parenthesis and left parenthesis 2 comma 40 right parenthesis

(0,25)
and (5,60)
left parenthesis 0 comma 25 right parenthesis and left parenthesis 5 comma 60 right parenthesis

(5,60)
and (8,80)

1 answer

To determine which points can be used to find the linear equation that models the graph of the total cost versus the number of campers, we need to look for two points that will help us find the slope and intercept of the linear model.

  1. The point \((0, 25)\) typically represents the y-intercept of the graph (the total cost when there are 0 campers).
  2. The point \((2, 40)\) shows the total cost when there are 2 campers.
  3. The point \((3, 45)\) shows the total cost when there are 3 campers.
  4. The point \((5, 60)\) shows the total cost when there are 5 campers.
  5. The point \((8, 80)\) shows the total cost when there are 8 campers.

Considering the provided options:

  • Option 1: \((3, 45)\) and \((5, 60)\)
  • Option 2: \((0, 25)\) and \((2, 40)\)
  • Option 3: \((0, 25)\) and \((5, 60)\)
  • Option 4: \((5, 60)\) and \((8, 80)\)

To effectively create a linear equation, it is beneficial to include a point at the y-intercept \((0, 25)\) in combination with another point that provides another distinct value for the slope calculation.

Therefore, Option 3: \((0, 25)\) and \((5, 60)\) is the best choice because it includes the y-intercept as one of the points, which is essential for deriving the linear equation.

So the correct response would be:

(0, 25) and (5, 60).