Answer:
Part a) [tex]6x+4y=48[/tex]
Part b) The graph in the attached figure
Part c) (6,3) and (4,6)
Step-by-step explanation:
Part a) Write a linear equation to represent the number of items you can buy if she spends $48
Let
x ----> number of package of cupcakes you can buy
y ---> number of package of cookies you can buy
we know that
The number of package of cupcakes you can buy multiplied by it cost ($6 for a package) plus the number of package of cookies you can buy multiplied by it cost ($4 for a package) must be equal to $48
so
The linear equation that represent this problem is
[tex]6x+4y=48[/tex]
Part b) Graph the equation
To graph the line we need two points
Find the intercepts
Find the x-intercept (value of x when the value of y is equal to zero)
For y=0
[tex]6x+4(0)=48[/tex] ----> [tex]x=8[/tex]
the x-intercept is the point (8,0)
Find the y-intercept (value of y when the value of x is equal to zero)
For x=0
[tex]6(0)+4y=48[/tex] ----> [tex]y=12[/tex]
the y-intercept is the point (0,12)
Plot the intercepts and join the points to graph the line
see the attached figure
Part c) State two possible solutions in the context of the problem
1) First possible solution
the ordered pair (6,3)
That means
You can buy 6 package of cupcakes and 3 package of cookies
Verify in the linear equation
[tex]6(6)+4(3)=48[/tex]
[tex]48=48[/tex] ---> is true
therefore
The ordered pair is a solution of the linear equation
2) Second possible solution
the ordered pair (4,6)
That means
You can buy 4 package of cupcakes and 6 package of cookies
Verify in the linear equation
[tex]6(4)+4(6)=48[/tex]
[tex]48=48[/tex] ---> is true
therefore
The ordered pair is a solution of the linear equation
