Question

choose the equation best models the data(12,39)(42,132)y=6.1x+1.8y=31/10 x+132y=61/10 x+132y=3.1x+1.8

Answer 1

`y=3.1x+1.8`

Step-by-step explanation

Step 1

find the slope of the line

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

where P1 and P2 are 2 coordinates of the line

Let

P1=(12,39)

P2=(42,132)

replace,

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(132-39)/(42-12) \\ \text{slope}=(93)/(30) \\ \text{slope}=3.1 \end{gathered}`

Step 2

find the equation of the line,use

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

replace

`\begin{gathered} y-39=3.1(x-12) \\ y-39=3.1x-37.2 \\ \text{add 39 in both sides} \\ y-39+39=3.1x-37.2+39 \\ y=3.1x+1.8 \end{gathered}`

I hope this helps you