Question

The table represents a function.

Answer 1

We have to complete the statement:

" The rate of change in the function y=x+4 is ______ the rate of change of the function represented in the table."

Let us consider the function represented in table.

The coordinates given in the table are:

(0,6) (2,8) (4,10) and (6,12)

Consider the first two coordinates (0,6) and (2,8)

$x_{1}=0 , y_{1}=6, x_{2}=2 , y_{2}=8$

Equation of line is given by $(y-y_{1})=m(x-x_{1})$

where 'm' is slope(rate of change) is given by the formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, $m = \frac{8-6}{2-0}=1$

So, equation of line is :

(y-6)= 1 (x-0)

y-6=x

y=x+6

Comparing it with standard equation of line y=mx+c with slope 'm'.

So, we get m(Rate of change)=1.

Now,

We will find the rate of change(slope) in the function y=x+4

Comparing it with standard equation of line y=mx+c with slope 'm'.

So, we get m(Rate of change)=1.

So, " The rate of change in the function y=x+4 is equal to the rate of change of the function represented in the table.