Assuming a linear relationship between X and Y, find the slope of the line to write down an equation of the form:
[tex]y=mx+b[/tex]where m is the slope of the line and b is the y-intercept.
Take two pairs of values to calculate the slope. Use the pairs (2,8) and (4,14):
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{14-8}{4-2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]Substitute m=3 into the equation, as well as the values of one of the pairs. Take x=2 and y=8. You can then find the value of b:
[tex]\begin{gathered} 8=3(2)+b \\ =6+b \\ \Rightarrow b=2 \end{gathered}[/tex]Substitute b=2 and m=3 to find the equation of that linear relation:
[tex]y=3x+2[/tex]Substitute x=7 to find the missing value of y:
[tex]\begin{gathered} y=3\cdot7+2 \\ =21+2 \\ =23 \end{gathered}[/tex]Therefore, the equation of the table is y=3x+2 and the missing value of y when x=7 is 23.
