Answer:
Part a) [tex]y=1.5x+12[/tex]
Part b) The total price for 10 photos is equal to $27
Part c) see the explanation
Step-by-step explanation:
Part a) write a function rule that models the graph
Let
x ----> the number of photos
y ---> the total price in dollars
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or the unit rate of the linear equation
b is the y-intercept or initial value
In this problem the y-intercept is the point (0,12)
so
[tex]b=\$12[/tex]
Looking at the graph
take any two points on the line
(0,12) and (4,18)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{18-12}{4-0}[/tex]
[tex]m=\frac{6}{4}=\$1.5\ per\ photo[/tex]
Find the equation of the function
we have
[tex]m=\$1.5\ per\ photo[/tex]
[tex]b=\$12[/tex]
substitute
[tex]y=1.5x+12[/tex]
Part b) Explain what the coordinate (10,27) means in context of the problem
Remember that
x ----> the number of photos
y ---> the total price in dollars
therefore
That means ----> The total price for 10 photos is equal to $27
Part c) Prove that (10,27) is a solution to the function rule
we have
x=10,y=27
Remember that
If a ordered pair is a solution of the function rule, then the ordered pair must satisfy the function rule
substitute the value of x and the value of y in the function rule and analyze the result
[tex]27=1.5(10)+12[/tex]
[tex]27=27[/tex] ----> is true
therefore
The ordered pair is a solution of the function rule
