Given the table for x, tickets sold and y, money earned:

Question

x - tickets 4 9 8 5 7
y - $ earned 48 108 96 60 84

a. Every ticket sold is _____________ dollars earned.

b. dollors1 ticket is called a ____________

c. this relationship is _______________ because 0 tickets sold is_________ dolloars earned

Answer 1

Let's analyze the data given in the table:

• Tickets sold (x): 4, 9, 8, 5, 7
• Money earned (y): 48, 108, 96, 60, 84

a. Every ticket sold is $12 earned. (You can calculate this by dividing the total money earned (y) by the number of tickets sold (x) for any of the pairs.)

For example, for the pair where 4 tickets were sold: \[ \text{Money earned} = $48 \quad \Rightarrow \quad \frac{48}{4} = 12 \text{ dollars per ticket} \]

b. Dollar per ticket is called a price per ticket or unit price.

c. This relationship is linear because 0 tickets sold is $0 dollars earned. (When there are no tickets sold, there is no money earned, which suggests a linear relationship through the origin.)

Answer 2

Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.

Answer 3

To find the equation of the line that shows the proportional relationship between tickets sold and money earned, we can use the information that you've provided.

Given that:

• You discovered that every ticket sold earns $12, this indicates that the slope (m) of the line is \(12\).

Since the line passes through the origin (0,0), the equation of the line can be expressed as: \[ y = mx \]

Substituting the value of \(m\) (which is 12): \[ y = 12x \]

Therefore, the equation of the line that describes the proportional relationship between the number of tickets sold (x) and the money earned (y) is: \[ y = 12x \]

Answer 4

b. Write an equation to show the relationship between x and y.

Answer 5

To express the relationship between \(x\) (tickets sold) and \(y\) (money earned) in the form of an equation, we can use the slope-intercept form of a linear equation.

From our previous discussion, we determined that every ticket sold earns $12. Thus, the relationship can be expressed as:

\[ y = 12x \]

This equation means that for every ticket sold (x), the total money earned (y) is 12 times the number of tickets sold.

In summary, the equation showing the relationship between \(x\) and \(y\) is:

\[ y = 12x \]