Question

The graph below represents Function R

The equation 3x-1 represents Function S.
Which statement about Functions R and S is true?
A.The rate of change of Function R is less than the rate of change of Function S because 2/3<3.
B.The rate of change of Function R is less than the rate of change of Function S because 2<3
C.The rate of change of Function R is equal to the rate of change of Function S because both are 1
D.The rate of change of Function R is greater than the rate of change of Function S because 1>-1.

Answer 1

Option A: The rate of change of Function R is less than the rate of change of Function S because
`(2)/(3)<3` is true.

Explanation:

The function
`S=3x-1`

The equation for function R can be determined using the slope formula,

`y=mx+b`

The y-intercept is the value of y, when x = 0.

Thus, the y-intercept is
`b=1`.

To determine the slope, let us substitute the coordinates
`(0,1)` and
`(3,3)`.

Because, the points on the straight line have the same slope.

Thus, we have,

`m=(y_2-y_1)/(x_2-x_1) \\m=(3-1)/(3-0) \\m=(2)/(3)`

Thus,
`m=(2)/(3)` and
`b=1`

Let us substitute these values in the formula
`y=mx+b`, we get,

`y=(2)/(3) x+1`

Hence, the equation of R is
`y=(2)/(3) x+1`

The equation of S is
`y=3x-1`

Comparing the slope of these two equations, we have,

`(2)/(3)<3`

This means that the slope of R is less than the slope of S.

Hence, The rate of change of Function R is less than the rate of change of Function S because
`(2)/(3)<3`

Thus, Option A is true.