Question

Determine any data values that are missing from the table, assuming that the data represent a linear function. X: 1 2 4 Y: 2 6 a. 2b 10C. 14d. 16

Answer 1

Given the points (1,2) and (2,6), we can find the relation function with the slope-point formula for the equation of a line:

`\begin{gathered} \text{slope:} \\ m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(6-2)/(2-1)=(4)/(1)=4 \\ m=4 \\ y-y_1=m(x-x_1) \\ \Rightarrow y-2=4(x-1)=4x-4 \\ \Rightarrow y=4x-4+2=4x-2 \\ y=4x-2 \end{gathered}`

we have that the linear function is y=4x-2. Then for x=4 we have the following:

`\begin{gathered} x=4 \\ \Rightarrow y=4\cdot4-2=16-2=14 \\ y=14 \end{gathered}`

therefore, the missing value is y=14