Answer:
Part a) The weekly cost of food for a family of four in 1997 was $153.09
Part b) [tex]y=4.83x+153.09[/tex]
Part c) [tex]\$215.88[/tex]
Step-by-step explanation:
Part a. What was the weekly cost of food for a family of four in 1997?
Let
y ---->the weekly cost of food for a family of four
x ---> the number of years since 1997
we know that
The linear equation in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
In this problem we have a linear function between variable x and variable y
In 2004, the weekly cost of food for a family of four was $186.90
so
In the year 2004
The value of x is equal to
x=2004-1997=7 years
we have
[tex]point\ (7,186.90)[/tex]
[tex]m=\$4.83\ per\ year[/tex]
substitute
[tex]y-186.90=4.83(x-7)[/tex] ----> equation in point slope form
Remember that the year 1997 is when the value of x is equal to zero
so
For x=0
[tex]y-186.90=4.83(0-7)[/tex]
solve for y
[tex]y=4.83(-7)+186.90[/tex]
[tex]y=153.09[/tex] -----> y-intercept or initial value
therefore
The weekly cost of food for a family of four in 1997 was $153.09
Part b. Write an equation that gives the weekly cost of food for a family of four as a function of the number of years since 1997
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept or initial value
we have
[tex]m=\$4.83\ per\ year[/tex]
[tex]b=\$153.09[/tex] ----> initial value in 1997
substitute
[tex]y=4.83x+153.09[/tex]
Part c. Find the weekly cost of food for a family of four in 2010 assuming the same rate of increase
In the year 2010
x=2010-1997=13 years
substitute in the linear equation
[tex]y=4.83(13)+153.09=215.88[/tex]
