Question

(-3,1) perpendicular to y=2/5x-4

Answer 1

(-3, 1)             y = 2/5x - 4 
 x₁  y₁              slope (m) = 2/5x

Since the equation we are looking for is perpendicular to y = 2/5x - 4, we need to find the opposite reciprocal slope. We have to flip the slope upside down and turn it negative.

2/5 ⇒ 5/2 ⇒ -5/2

So far, we have the equation y = -5/2.

Now, we need to find the y intercept by plugging in the given point into point slope form, which is...

y - y₁ = m(x - x₁) 

The subscripts in the y and x are just the x and y in (-3,1). They are just placeholders, not exponents.

y - 1 = -5/2(x + 3)
 y - 1 = -5/2x - 15/2
   + 1               +     1
------------------------------
 y = -5/2x - 13/2 ⇒ final equation