Question

Using a minimum of three points, create two linear functions.

Answer 1

First, we can take the points (0,10), (-4,8) and (2,11) to find the slope, and then find the linear equation using the third point.

`\begin{gathered} (x_1,y_1)=(0,10) \\ (x_2,y_2)=(-4,8) \\ m=(8-10)/(-4-0)=(-2)/(-4)=(1)/(2) \\ m=(1)/(2) \end{gathered}`

now that we have that the first slope is m = 1/2, we can use the point (2,11) to find the linear equation:

`\begin{gathered} y-11=(1)/(2)(x-2)=(1)/(2)x-1 \\ \Rightarrow y=(1)/(2)x-1+11=(1)/(2)x+10 \\ y=(1)/(2)x+10 \end{gathered}`

we can see that the three points fit the equation:

`\begin{gathered} (0,10) \\ 10=(1)/(2)(0)+10\Rightarrow10=10 \\ (-4,8) \\ 8=(1)/(2)(-4)+10=-2+10=8 \\ (2,11) \\ 11=(1)/(2)(2)+10=1+10=11 \end{gathered}`

if we do the same with the points (-3,-3), (-1,1) and (2,7), we get:

`\begin{gathered} m=(1-(-3))/(-1-(-3))=(1+3)/(-1+3)=(4)/(2)=2 \\ \Rightarrow y-7=2(x-2)=2x-4 \\ \Rightarrow y=2x-4+7=2x+3 \\ y=2x+3 \end{gathered}`

therefore, the two linear functions found are y = 1/2 x +10 and y=2x+3