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 $\frac{2}{3}<3$ 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,

$m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{3-1}{3-0} \\m=\frac{2}{3}$

Thus, $m=\frac{2}{3}$ and $b=1$

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

$y=\frac{2}{3} x+1$

Hence, the equation of R is $y=\frac{2}{3} x+1$

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

Comparing the slope of these two equations, we have,

$\frac{2}{3}<3$

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 $\frac{2}{3}<3$

Thus, Option A is true.