Two lines are perpendicular when the multiplication of their slopes is equal to -1.
The slope of the line: y = 2x + 1 is 2, then the slope of a perpendicular line will be:
[tex]\begin{gathered} m\cdot2=-1 \\ m=-\frac{1}{2} \end{gathered}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope, and b is the y-intercept.
Replacing into the equation with m = -1/2 and point (1, 8), we get:
8 = -1/2(1) + b
8 = -1/2 + b
8 + 1/2 = b
17/2 = b
Then, the equation is:
y = -1/2x + 17/2
