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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?

User Freebie
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1 Answer

12 votes

Answer:


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

User Tal Ohana
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