Question

1. Judy took $42 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $6. The price of each drink was half the price of a bag of popcorn.

(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks.

(b) Explain your graph.

Answer 1

The graph in the attached figure

Explanation:

Sketch the graph that represents the situation and label the intercepts

Let

x ------> the number of bags of popcorn

y -----> the number of drinks.

we know that

The price for each bag of popcorn was $6

The price of each drink was half the price of a bag of popcorn

so

The price of each drink was (1/2)$6=$3

The total bags of popcorn multiplied by $6 plus the number of drinks multiplied by $3 must be equal $42

The equation that represent this situation is

`6x+3y=42`

using a graphing tool

see the attached figure

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

`6(0)+3y=42`

`y=14`

The y-intercept is the point (0,14)

That means -----> The number of drinks that Judy can buy when the number of bags of popcorn is equal to zero

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

`6x+3(0)=42`

`x=7`

The x-intercept is the point (7,0)

That means ----->The number of bags of popcorn that Judy can buy when the number of drinks is equal to zero