Question

exceeding: the money made from selling tickets is below, where x is the number of tickets sold and y is the amount of money made: x 6 7 8 9 y 10 12 14 16 answer the following questions about the situation above: graph the table: why is this situation linear? what does the slope of the line mean in this context? if the slope were larger, what would that mean for the situation?

Explanation:

Step1: Identify points

The points from the table are (6, 10), (7, 12), (8, 14), (9, 16).

Step2: Graph the points

On the coordinate - plane, mark the x - values (number of tickets) on the x - axis and y - values (amount of money) on the y - axis and plot the points.

Step3: Determine linearity

The change in y for a unit change in x is constant. $\Delta y=12 - 10=2$ when $\Delta x = 7 - 6 = 1$. Since the rate of change (slope) is constant, it is linear.

Step4: Calculate slope

The slope $m=\frac{\Delta y}{\Delta x}=\frac{12 - 10}{7 - 6}=2$. In this context, the slope means that for each additional ticket sold, the amount of money made increases by 2 dollars.

Step5: Analyze larger slope

If the slope were larger, it would mean that for each additional ticket sold, the amount of money made would increase by a larger amount. For example, if the slope was 3, for each extra ticket sold, the money made would increase by 3 dollars instead of 2 dollars.

Answer:

• To graph the table: Plot the points (6, 10), (7, 12), (8, 14), (9, 16) on a coordinate - plane with x as the number of tickets and y as the amount of money.
• This situation is linear because the rate of change (slope) between the number of tickets sold and the amount of money made is constant.
• The slope of the line means that for each additional ticket sold, the amount of money made increases by 2 dollars.
• If the slope were larger, it would mean that for each additional ticket sold, the amount of money made would increase by a larger amount.