Question

Which function has the greater rate of change?

Function 1 : y= 5/6x+10
Function 2 pictured below:

Answer 1

Function 1

Explanation:

The rate of change is measured by the slope m

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y =
`(5)/(6)` x + 10 ← is in slope- intercept form

with slope m =
`(5)/(6)`

Calculate the slope of Function 2 using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 14.25) and (x₂, y₂ ) = (1, 15.75) ← 2 ordered pairs from the table

m =
`(15.75-14.25)/(1+1)` =
`(1.5)/(2)` = 0.75 =
`(3)/(4)`

To compare the 2 fractions we require them to have a common denominator.

`(5)/(6)` =
`(10)/(12)` and
`(3)/(4)` =
`(9)/(12)`

`(10)/(12)` >
`(9)/(12)`

Thus Function 1 has the greater rate of change