Question

Two functions are represented in different ways.

Function 1:

Let x = number of hours worked

Let y = total pay in dollars

y = 20x + 15



Function 2: A babysitting club charges a $25 flat rate and $10 for each hour.



Which statements are true?

Select each correct answer.

Function 1 has a greater rate of change than function 2.

Function 2 has a greater rate of change than function 1.

Function 1 has a greater y-intercept than function 2.

Function 2 has a greater y-intercept than function 1.

Answer 1

Well function two given the information provided would be:

y=10x+25

And since a line of y=mx+b means that it has a slope of m and a y-intercept of b we can say that in comparison to y=20x+15:

Function one has a greater rate of change (slope) than function two (20>10)

Function two has a greater y intercept than function one (25>15)

Answer 2

function 1 has greater rate of change than function 2.

function 2 has a greater y-intercept than function 1.

Explanation:

Function 1 is given by: y=20x+15

and Function 2 is given by:y=10x+25

as we know that the rate of change of a equation is same as slope of a equation and the slope of the general form of the equation of the type y=mx+c is given by 'm'.

for function 1 the slope is:20

and for the function 2 the slope is:10

so the slope of function 1 is greater than the slope of the function 2.

Hence function 1 has greater rate of change than function 2.

also the y-intercept of a line is the value of y for which x=0.

for function 1 when x=0 y=15

and for function 2 when x=0 y=25.

Hence, the y-intercept for the function 2 is greater than that of function 1.