Question

Complete the table representing a linear function.

Answer 1

Explanation:

(1,0) (5,40)

Using these coordinates we find the line equation y=mx+b:

`\displaystyle\\m=(y_2-y_1)/(x_2-x_1) \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=0\ \ \ \ y_2=40\\\\m=(40-0)/(5-1) \\\\m=(40)/(4) \\\\m=10\\\\Thus,\ y=10x+b \ \ \ \ (1)\\`

We substitute the value of coordinate (1,0) into equation (1):

`0=10(1)+b\\\\0=10+b\\\\-10=b\\\\Thus, \ b=-10\\\\Hence,\\\\ y=10x-10\\\\x=2\\\\y=10(2)-10\\\\y=20-10\\\\y=10\\\\Thus,(2,10)\\\\y=90\\\\90=10x-10\\\\100=10x`

Divide both parts of the equation by 10:

`10=x\\\\Thus, (10,90)`

x | y

-----------------

1 | 0

------------------

2 | 10

------------------

5 | 40

------------------

10 | 90

Answer 2

x y

1 0

2 10

5 40

10 90

Explanation:

In a linear function, every time x is increased by 1, y is increased by a set amount. The only two complete rows in the table are when x = 1 and x = 5. x is increased four times in that interval while y has increased by 40(40 - 0). This means that every time x increases by 1, y increases by 10(40/4).

Therefore, when x is 2, y will be 10.

To get to ninety, 10 will needed to be added to 0(when x=1) 9 times. 1 + 9 is 10, so x = 10 when y = 90.