Question

Please find the linear function that best fits problem 11

Answer 1

A linear function is having the form

`\begin{gathered} y=ax+b \\ \text{where } \\ a=\text{slope, b=y-intercept } \end{gathered}`
`\begin{gathered} \text{when x=o, y=}1 \\ \text{substitute into the equation } \\ y=ax+b \\ 1=a(0)+b \\ \text{Hence } \\ b=1 \end{gathered}`

Similarly, when x=-2, y=-5

Substitute into the equation for a linear function

`\begin{gathered} y=ax+b \\ -5=a(-2)+1 \\ -5=-2a+1 \\ \text{subtract 1 from both sides } \\ -5-1=-2a \\ -6=-2a \end{gathered}`
`\begin{gathered} \text{divide both sides by -2} \\ -(6)/(-2)=-(2a)/(-2) \\ \text{Then} \\ a=3 \end{gathered}`

Hence

`\begin{gathered} a=3,\text{ b=1} \\ \end{gathered}`

The linear function becomes

Y = 3x + 1