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Where is the problem of air pollution most severe?

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1 answer:

Soloha48 [4]3 years ago

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New york state i believe

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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-i

nikklg [1K]

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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