Two lines are perpendicular when the multiplication of their slopes is equal to -1. The slope of y = 5x - 2, is 5, then:
[tex]\begin{gathered} m\cdot5=-1 \\ m=-\frac{1}{5} \end{gathered}[/tex]Then, the slope of the new line: -1/5
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Replacing with point (-10, 6) and m = -1/5, we get:
6 = (-1/5)(-10) + b
6 = 2 + b
6 - 2 = b
4 = b
Then, the equation is: y = -1/5x + 4