Answer:
see the explanation
the graph in the attached figure
Step-by-step explanation:
Let
x ----> the number of bags of popcorn
y ---> the number of drinks
we know that
The price of each bag of popcorn was $5
The price of each drink was half the price of a bag of popcorn
so
The price of each drink was $5/2=$2.5
Remember that
The number of bags of popcorn and drinks Judy bought, multiplied by their prices, should equal $30.
The linear equation that represent this situation is
[tex]5x+2.5y=30[/tex]
To graph the linear equation , find the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
In the context of the situation, the y-intercept represent the number of drinks Judy can buy when the number of bags of popcorn equals zero
so
For x=0
[tex]5(0)+2.5y=30[/tex]
[tex]2.5y=30[/tex]
[tex]y=12\ drinks[/tex]
The y-intercept is the point (0,12)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
In the context of the situation, the x-intercept represent the number of bag of popcorn Judy can buy when the number of drinks equals zero
so
For y=0
[tex]5x+2.5(0)=30[/tex]
[tex]5x=30[/tex]
[tex]x=6\ bags\ of\ popcorn[/tex]
The x-intercept is the point (6,0)
To graph the line plot the intercepts and join the points
using a graphing tool
The graph in the attached figure
