Question

Options for the first box are y=1.06x -6, y=1.2x-4, y=1.5x-7, 1.4x-8 Options for the second box are:36, 33, 40, 30

Answer 1

From the given table we will use the two points (10, 4) and (15, 10) to find the slope of the line

The rule of the slope is

`m=(y2-y1)/(x2-x1)`

Let (x1, y1) = (10, 4) and (x2, y2) = (15, 10)

`\begin{gathered} m=(10-4)/(15-10) \\ m=(6)/(5) \\ m=1.2 \end{gathered}`

The form of the linear equation is

`y=mx+b`

substitute the value of m

`y=1.2x+b`

To find b substitute x by 10 and y by 4

`\begin{gathered} x=10,y=4 \\ 4=1.2(10)+b \\ 4=12+b \end{gathered}`

Subtract 12 from both sides

`\begin{gathered} 4-12=12-12+b \\ -8=b \end{gathered}`

The equation of the line best fit is

`\begin{gathered} y=1.2x+(-8) \\ y=1.2x-8 \end{gathered}`

At x = 40, substitute x by 40

`\begin{gathered} y=1.2(40)-8 \\ y=48-8 \\ y=40 \end{gathered}`

The expected number of games own is 40 games