Question

Shauna is going fishing. She records how many worms she has left at the start of each hour in the table below. Write a linear function

rule for the data.
0
1
3
4
2
5
у
9
7
3
1
O FIX) - - 2x + 9
O f(x) = -2x - 6
Of(x) - 2x - 6
O f(x) = 2x + 9

Answer 1

`f(x)= -2x + 9`

Explanation:

The table is not properly formatted:

We have:

x ------- y

0 ------- 9

1 ------- 7

2 ------- 5

3 ------- 3

4 ------- 1

Required

Determine the linear equation

Since, it is a linear equation.

We need to first determine the slope.

Take any to corresponding values of x and y

`(x_1,y_1) = (0,9)`

`(x_2,y_2) = (4,1)`

Slope is then calculated as thus:

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

`m = (9 - 1)/(0 - 4)`

`m = (8)/(- 4)`

`m = -2`

The linear equation is then calculated as thus:

`y - y_1 = m(x - x_1)`

`y - 9 = -2(x - 0)`

`y - 9 = -2x`

Add 9 to both sides

`y - 9 + 9= -2x + 9`

`y = -2x + 9`

`f(x)= -2x + 9`