Question

1. An input-output table has constant differences. When the input is 3, the output is 10. When the input is 7, the output is 24. a. Find the constant difference. b. Find the output when the input is 0. C. Find the linear function that fits the table.

Answer 1

a)7,17

b)-25

c)

`y=3.5x-25`

Step-by-step explanation

table

a) differences

10-3=7

24-7=17

Step 1

find the slope

`\begin{gathered} \text{slope}=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}`

Let

P1(3,10)

p2(7,24)

replace,

`\begin{gathered} \text{slope}=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(24-10)/(7-3)=(14)/(4)=(7)/(2) \\ \text{slope}=(7)/(2) \end{gathered}`

Step 2

find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-10=(7)/(2)(x-10) \\ y-10=(7)/(2)x-(70)/(2) \\ y=(7)/(2)x-(70)/(2)+10 \\ y=3.5x-25 \end{gathered}`

Step 3

when x=0

`\begin{gathered} y=3.5x-25 \\ y=3.5\cdot0-25 \\ y=-25 \end{gathered}`

I hope this helps you