Answer::
[tex]y=x+16[/tex]Explanation:
Given two points on a line:
[tex]\begin{gathered} (x_1,y_1)=(2,18) \\ \left(x_2,y_2\right)=\left(7,23\right) \end{gathered}[/tex]We use the two-point formula below to find the linear function rule.
[tex]$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$[/tex]Substitute the values:
[tex]\begin{gathered} \frac{y-18}{x-2}=\frac{23-18}{7-2} \\ \frac{y-18}{x-2}=\frac{5}{5} \\ \frac{y-18}{x-2}=1 \end{gathered}[/tex]Next, make y the subject:
[tex]\begin{gathered} y-18=x-2 \\ y=x-2+18 \\ y=x+16 \end{gathered}[/tex]The linear function rule is:
[tex]y=x+16[/tex]