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

A. Find and compare the slopes

B. Find and compare the y-intercept

C. Describe each function as proportional or non proportion

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

This is a linear equation in slope intercept form

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

Function 2

we know that

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

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

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

For x=0

Function 2

Find the equation in point slope form

we have

substitute

Convert to slope intercept form

isolate the variable y

For x=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 or

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

-----> is a non proportional linear function (because the line has a y-intercept)

Function 2

----> is a proportional linear equation (the line passes through the origin)

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

42%

step-by-step explanation:

we know,

total people = 60

total males = 25

percentage of males

= 25/60 × 100

= 25/6 × 10

= 25/3 × 5

= 125 / 3

= 41.

rounding of = 42%

happy to

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