Question

Write a rule for the function X -2 -1 0 1 2 Y 1/121 1/11 1 11 121

Answer 1

`y=(1330)/(121)x+1`

Explanation:

Linear functions are represented by the following equation:

`\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{ rate of change} \\ b=\text{ y-intercept} \end{gathered}`

The rate of change of a function is represented as follow:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \end{gathered}`

Given the points: (-2, 1/121) and (-1, 1/11):

`\begin{gathered} m=((1)/(11)-(1)/(121))/(-1-(-2)) \\ m=((1330)/(121))/(1) \\ m=(1330)/(121) \end{gathered}`

*Remember the y-intercept is when x=0. then the y-intercept of the function is 1.

Hence, the function is represented as.

`y=(1330)/(121)x+1`