Question

Write an equation perpendicular to x - 4y = 20 that passes through the point (4, -3)

Answer 1

y = - 4x + 13

Explanation:

In order to do this problem you would need a whole new equation, but you will use what is given to you:

instead of going with:

x - 4y = 20

Turn it into y = mx + b form, also known as slope-intercept form:

x - 4y = 20

-x = -x

_________

- 4y = 20 - x

Then divide both sides by - 4:

`(-4y)/(-4) = (-x + 20)/(-4)`

You will then get:

y =
`(1)/(4)x - 5`

From this equation we will only need the slope!

m || =
`(1)/(4)`

(This slope is for parallel)

but if you want perpendicular to the slope, then we need the negative reciprocal!

Negative reciprocal is a flipped version of the value that is negative, for example:

2 =
`-(1)/(2)`

Because
`(2)/(1)` = 2

Now we will find the perpendicular slope which is:

m ⊥ = - 4

Now substitute this slope into slope intercept form:

y = mx + b

(-3) = -4(4) + b

(Take away parentheses)

-3 = -16 + b

(Move - 3 to the other side, by making it positive, but what you do to one side, you do to the other)

= -13 + 6

(Move - 13 to the other side, by make - 13 into +13)

+13 = +13

________

13 = b

(This is you b, also known as you intercept)

Your answer is:

y = -4x + 13