Question

Linear functions can be used to find the price of a building based on its floor area below are two of these functions,

Answer 1

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

$y=40x+15,000$

This is a linear equation in slope intercept form

$y=mx+b$

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

$m=\ 40\ per\ ft^2$

Function 2

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

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

$m=\frac{56,000-32,000}{700-400}$

$m=\ 80\ per\ ft^2$

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

$y=40x+15,000$

For x=0

$y=40(0)+15,000=\ 15,000$

Function 2

Find the equation in point slope form

$y-y1=m(x-x1)$

we have

$m=80\\point\ (400,32,000)$

substitute

$y-32,000=80(x-400)$

Convert to slope intercept form

isolate the variable y

$y-32,000=80x-32,000\\y=80x$

For x=0

$y=80(0)=0$

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 $k=\frac{y}{x}$ or $y=kx$

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

$y=40x+15,000$ -----> is a non proportional linear function (because the line has a y-intercept)

Function 2

$y=80x$ ----> is a proportional linear equation (the line passes through the origin)