Given:
The slope of line, m=-5.
The line passes through point (x1, y1)=(6,2).
The point-slope form of the equation of a line can be expressed as,
[tex]\frac{y-y1}{x-x1}=m[/tex]Now, put the values of x1, y1 and m in the above equation to find the equation of the line.
[tex]\begin{gathered} \frac{y-2}{x-6}=-5 \\ y-2=-5(x-6) \\ y-2=-5x-5\times(-6) \\ y-2=-5x+30 \\ y=-5x+30+2 \\ y=-5x+32 \end{gathered}[/tex]Therefore, the equation of the line passing through (6,2) and having slope, m=-5, is y=-5x+32.
