Write the equation

through: (1, 5), perpendicular to

Two things must be performed to make an equation that satisfies this. First, we need to come up with a general equation that is perpendicular to the one in the problem. To do this, the reciprocal of the slope is calculated (negative inverse). The line that is perpendicular to y=1/8x + 2 has a slope of -8. This is what our equation looks like so far:

y’=-8x

This is good, but it doesn’t pass through (1,5). To make it do this, put the point in the equation and solve it - a point on a graph that intersects the line is a “solution” of the equation, so we need to solve for it!

y’ = -8x

(5) = -8(1)

Nope, 5 doesn’t equal -8. Let’s make the two sides equal by adding 13 to the right side.

y’ = -8x + 13

(5) = -8(1) + 13

5=5 - yes!

Our equation that is perpendicular to the one in the question and also passes through the point (1, 5) is y’=-8x + 13.

Hope this helps!