Solution:
The general equation of a line of slope m passing through a point A is expressed as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ (x_1,y_1)\text{ is the coordinate of the point A through which the line passes through} \end{gathered}[/tex]
Given that the line has a slope of 5, and passes through the (6, 22), we have
[tex]\begin{gathered} m=5 \\ x_1=6 \\ y_1=22 \end{gathered}[/tex]
thus,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-22=5(x-6) \end{gathered}[/tex]
Hence, the point-slope equation for the line is expressed as
[tex]y-22=5(x-6)[/tex]
