Question

Camille is making a graph that shows the proportional relationship between the amount of money collected, y, and the number of tickets sold, x. She correctly plots the point (300, 750).

Answer 1

A: The point (180, 450) is on the graph because $450 dollars will be collected if 180 tickets are sold.

C: The constant of proportionality is 750/300, which is equal to 2.5

D:The point (0, 0) is on the graph because on money is collected if no tickets are sold

F: The equation y = 2.5x represents this situation.

Explanation:

The complete question is

Camille is making a graph that shows the proportional relationship between the amount of money collected, y, and the number of tickets sold, x. She correctly plots the point (300,750).

Which of these statements are true? Choose all that apply.

A: The point (180, 450) is on the graph because $450 dollars will be collected if 180 tickets are sold.

B: The point (1, 0.4) is on the graph and identifies that the cost for each ticket is $0.40.

C: The constant of proportionality is 750/300, which is equal to 2.5.

D:The point (0, 0) is on the graph because on money is collected if no tickets are sold.

E: The point (5, 12.5) is not on the graph because it is impossible to sell 12.5 tickets.

F: The equation y = 2.5x represents this situation.

step 1

Find the linear equation

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

y ---> the amount of money collected

x ---> the number of tickets sold

we have the point (300,750)

Find the constant of proportionality k

`k=(750)/(300)=2.5`

so

`y=2.5x`

Verify all the statements

A: The point (180, 450) is on the graph because $450 dollars will be collected if 180 tickets are sold.

The statement is true

Because

Remember that

If a point is on the graph, the the point must satisfy the linear equation of the graph

substitute the value of x and the value of y of the point in the linear equation

`450=2.5(180)`

`450=450` ----> is true

B: The point (1, 0.4) is on the graph and identifies that the cost for each ticket is $0.40.

The statement is false

Because

For x=1

substitute in the linear equation

`y=2.5(1)`

`y=\$2.5`

The cost of each ticket is $2.5

C: The constant of proportionality is 750/300, which is equal to 2.5

The statement is true (see the explanation)

D:The point (0, 0) is on the graph because on money is collected if no tickets are sold.

The statement is true (see the explanation)

Because a proportional relationship passes through the origin

E: The point (5, 12.5) is not on the graph because it is impossible to sell 12.5 tickets

The statement is false

The point (5,12.5) is on the graph, because that means, for 5 tickets sold, the amount of money collected is $12.5

F: The equation y = 2.5x represents this situation.

The statement is true (see the explanation)