Question

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

Answer 1

Answer:

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

Step-by-step 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

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

substitute the values

$m=\frac{14+311}{1+12}$

$m=\frac{325}{13}$

$m=25$

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

$25$

Answer 2

Answer: The answer is D

Step-by-step explanation:

function 1 rate of change = 30

function 2 rate of change = 25

function 2: y = 25x − 11