Question

Let m and c represent constants with m nonzero. What is the equation of the line perpendicular to y=m(x+c) and with the same y-intercept?

Answer 1

`y = -(1)/(m)x + mc`

Step-by-step explanation:

Given

`y = m(x + c)`

Required

Determine an equation of a perpendicular line but with the same y intercept

`y = m(x + c)`

Open bracket

`y = mx + mc`

A linear equation is represented with:

`y = ax + b`

Where

`a = slope`

`b = y\ intercept`

By comparison:

`a = m`

`b = mc`

So, the slope of
`y = m(x + c)` is m

Because the new line is perpendicular to
`y = m(x + c)`, the relationship between their slopes is:

`a_2 = -(1)/(a_1)`

Where

`a_1 =` slope of the first equation

`a_2 =` slope of the second equation

Substitute m for
`a_1` in
`a_2 = -(1)/(a_1)`

`a_2 = -(1)/(m)`

Hence, the slope of the new equation is:
`-(1)/(m)`

From the question, we understand that they have the same y intercept.

So, the equation of the new equation is:

`y = -(1)/(m)x + mc`