Answer:
Part A) see the explanation
Part B) see the explanation
Part C) see the explanation
Step-by-step explanation:
The complete question in the attached figure
Part A) Find and compare the slopes
we have
Function 1
[tex]y=40x+15,000[/tex]
This is a linear equation in slope intercept form
[tex]y=mx+b[/tex]
where
y is the price of the building in thousands
x is the floor area in square foot
m is the slope
b is the y-intercept
we have
[tex]m=\$40\ per\ ft^2[/tex]
Function 2
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take two points from the data in the table
(400,32,000) and (700,56,000)
Remember that the price in the table is in thousands
substitute
[tex]m=\frac{56,000-32,000}{700-400}[/tex]
[tex]m=\$80\ per\ ft^2[/tex]
The slope of the Function 2 is greater than the slope of the Function 1
The slope of the Function 2 is two times the slope of the Function 1
Part B) Find and compare the y-intercept
we know that
The y-intercept is the value of y when the value of x is equal to zero
Function 1
[tex]y=40x+15,000[/tex]
For x=0
[tex]y=40(0)+15,000=\$15,000[/tex]
Function 2
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=80\\point\ (400,32,000)[/tex]
substitute
[tex]y-32,000=80(x-400)[/tex]
Convert to slope intercept form
isolate the variable y
[tex]y-32,000=80x-32,000\\y=80x[/tex]
For x=0
[tex]y=80(0)=0[/tex]
The y-intercept of the function 1 is $15,000 and the y-intercept of the function 2 is zero (the line passes through the origin)
Part C) Describe each function as proportional or non proportion
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
so
Function 1
[tex]y=40x+15,000[/tex] -----> is a non proportional linear function (because the line has a y-intercept)
Function 2
[tex]y=80x[/tex] ----> is a proportional linear equation (the line passes through the origin)
