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
![5x+2.5y=30](https://tex.z-dn.net/?f=5x%2B2.5y%3D30)
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
![5(0)+2.5y=30](https://tex.z-dn.net/?f=5%280%29%2B2.5y%3D30)
![2.5y=30](https://tex.z-dn.net/?f=2.5y%3D30)
![y=12\ drinks](https://tex.z-dn.net/?f=y%3D12%5C%20drinks)
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
![5x+2.5(0)=30](https://tex.z-dn.net/?f=5x%2B2.5%280%29%3D30)
![5x=30](https://tex.z-dn.net/?f=5x%3D30)
![x=6\ bags\ of\ popcorn](https://tex.z-dn.net/?f=x%3D6%5C%20bags%5C%20of%5C%20popcorn)
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