Question

What is the equation or rule that describes the following relationship

Answer 1

First, we find the slope

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

Where,

`\begin{gathered} x_1=-1 \\ x_2=1 \\ y_1=-1 \\ y_2=3 \end{gathered}`
`m=(3-(-1))/(1-(-1))=(3+1)/(1+1)=(4)/(2)=2`

Then, we use the point-slope formula to find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=2(x-(-1)) \\ y+1=2(x+1) \\ y+1=2x+2 \\ y=2x+2-1 \\ y=2x+1 \end{gathered}`

Hence, the answer is D.