Question

1. Judy took $45 with her to spend on popcorn and drinks for herself and friends at the movie

theater. The price for each bag of popcorn was $5 and the price for each drink was $3.
This can be represented by the equation 5x + 3y = 45 where x represents the number of bags of popcorn
and y represents the number of drinks (this assumes she will spend all $45).
a) Find the x and y intercepts of the equation.
Show how you found the x-intercepts
b) Use your intercepts to sketch the graph
c) Use your graph to find another combination of popcorn
Find the correct x and y intercepts

Answer 1

a) The x- and y-intercepts are (9, 0) and (0, 15), respectively. b) The graph is a line through those points (9, 0) and (0, 15) as shown below, c) Another combo is (6, 5), indicating 6 popcorn bags and 5 drinks for $45.

How to plot a graph using the x-intercept and the y-intercept?

a) To find the x-intercept, set y = 0 in the equation and solve for x:

5x + 3(0) = 45

Solving for x, we get:

5x = 45

x = 9

So, the x-intercept is (9, 0).

To find the y-intercept, set x = 0 in the equation and solve for y:

5(0) + 3y = 45

Solving for y, we get:

3y = 45

y = 15

So, the y-intercept is (0, 15).

b) Plot the x-intercept (9, 0) and the y-intercept (0, 15) on a graph and draw a line through these points as shown in the image attached below.

c) On the graph, find a point that lies on the line other than the intercepts. This represents another combination of popcorn and drinks, such as point A in the graph below which is at (6, 5). This means 6 bags of popcorn and 5 drinks would also cost $45.