Question

The table represents a function.

x y
0 −5
2 1
3 4
5 10

Complete the statement by selecting from the drop-down menu.
The rate of change in the function ​ y=x−6 ​ is
the rate of change of the function represented in the table.
chocies greater than, equal and less than

Answer 1

The correct option is 3. The rate of change in the function ​y=x-6​ is less than the rate of change of the function represented in the table.

Explanation:

The given table represents a function.

Choose any two points from the table. The two points are (0,-5) and (2,1).

Slope of a line is

m=\frac{y_2-y_1}{x_2-x_1}

Slope of the function that is represented by the table, is

m=\frac{1-(-5)}{2-0}=\frac{6}{2}=3

Therefore the rate of change of function is 3.

The given function is

​y=x-6

It is a slope intercept form of a line.

y=mx+b

Where m is the slope and b is y-intercept.

Therefore the slope of the given function is 1.

Since 1<3, therefore rate of change in the function ​y=x-6​ is less than the rate of change of the function represented in the table. Option 3 is correct.

Answer 2

The correct option is 3. The rate of change in the function ​
`y=x-6`​ is less than the rate of change of the function represented in the table.

Explanation:

The given table represents a function.

Choose any two points from the table. The two points are (0,-5) and (2,1).

Slope of a line is

`m=(y_2-y_1)/(x_2-x_1)`

Slope of the function that is represented by the table, is

`m=(1-(-5))/(2-0)=(6)/(2)=3`

Therefore the rate of change of function is 3.

The given function is

​
`y=x-6`

It is a slope intercept form of a line.

`y=mx+b`

Where m is the slope and b is y-intercept.

Therefore the slope of the given function is 1.

Since 1<3, therefore rate of change in the function ​
`y=x-6`​ is less than the rate of change of the function represented in the table. Option 3 is correct.