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love history [14]
3 years ago
13

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-i

ntercept?
Geography
1 answer:
nikklg [1K]3 years ago
8 0

Answer:

y = -\frac{1}{m}x + mc

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 = -\frac{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 = -\frac{1}{a_1}

a_2 = -\frac{1}{m}

Hence, the slope of the new equation is: -\frac{1}{m}

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

So, the equation of the new equation is:

y = -\frac{1}{m}x + mc

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