Question

Find an equation for the line passing through the point (6,1) and perpendicular to the line y=4x-2

Answer 1

y = -1/4x + 2.5

or

y = -1/4x + 5/2

Explanation:

First we know that a perpendicular line is one that intersects at a 90-degree angle. This is simply the negative inverse of the slope in our case. So, 4 turns into -1/4 and that is our new slope. Next we know that we want it to pass through the point (6,1). Right now our equation is y = -1/4x + b. We can plug (6,1) into this equation and solve.

1 = -1/4(6) + b

1 = -6/4 + b

4/4 + 6/4 = 10/4

10/4 = b

simplify: 5/2 or 2.5 = b

Now we have our y-intercept, so we can complete our equation.

y = -1/4x + 2.5

or

y = -1/4x + 5/2