Question

Write an equation perpendicular to the line y=1/4x -9 and passes through (1,1)

Answer 1

Perpendicular to $\text{y} = \dfrac{1}{4}\text{x} - 9$ ; passes through (1, 1)

Using y = mx+b, we can find the slope!

$\dfrac{1}{4}$ is in the "m" spot from slope-intercept form, so we know that $\dfrac{1}{4}$ is our slope.

However, all equations perpendicular to a line must have a negative reciprocal of the slope. Keep in mind that a negative reciprocal is simply a number that is flipped and is either given a negative or gets a negative removed.

$\dfrac{1}{4}$ now turns into -4, thus giving us a new slope of -4.

Now, using this equation y - y₁ = m (x - x₁), let's plug & chug!

Note : use (1, 1) as your $\dfrac{x}{y}$ & -4 as your slope.

y - (1) = -4(x - 1)

Simplify.

y - 1 = -4x + 4