Question

Two linear functions of x are shown. Which Statement about the functions is true?

Answer 1

Answer: The answer is D

Explanation:

function 1 rate of change = 30

function 2 rate of change = 25

function 2: y = 25x − 11

Answer 2

Option D. The rate of change of function 2 is less than the rate of change of the function 1

Explanation:

step 1

Find the rate of change and the y-intercept of the function 1

we have

`y=30x+19`

This is the equation of the line in slope intercept form

where

the slope is m=30

the y-intercept is b=19

Remember that the slope is the same that the rate of change

so

The rate of change of the function 1 is
`m_1=30`

The y-intercept of the function 1 is
`b_1=19`

step 2

Find the slope of the function 2

From the data in the table take two points

(-12,-311) and (1,14)

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

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(14+311)/(1+12)`

`m=(325)/(13)`

`m=25`

step 3

Find the equation of the function 2 in slope intercept form

`y=mx+b`

we have

`m=25`

`point\ (1,14)`

substitute

`14=25(1)+b`

solve for b

`b=14-25`

`b=-11`

The equation of the function 2 is

`y=25x-11`

so

The rate of change of the function 2 is
`m_2=25`

The y-intercept of the function 2 is
`b_2=-11`

Verify each statement

case A) Function 2 can be described by the equation y=25x-100

The statement is false

Because the equation of the function 2 is
`y=25x-11`

case B) Function 2 can be described by the equation y=13x-11

The statement is false

Because the equation of the function 2 is
`y=25x-11`

case C) The y-intercept of function 1 is less than the y-intercept of the function 2

The statement is false

Because, the y-intercept of function 1 is greater than the y-intercept of the function 2

`19 > -11`

case D) The rate of change of function 2 is less than the rate of change of the function 1

The statement is true

`25 <30`