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# coordinates

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What is an equation of the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6?

Apr 1, 2020

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Long way:  find the slope of the original line and use the point-slope form:

Original line:  5x - 2y  =  6

solve for y:     -2y  =  -5x + 6

y  =  (5/2)x - 3

slope  =  5/2

Use point-slope form to find the equation of the new line:

y - y1  =  m(x - x1)

--->     y - -4  =  (5/2)·(x - -2)

y + 4  =  (5/2)(x + 2)

y + 4  =  (5/2)x + 5

y  =  (5/2)x + 1

Rewriting:  2y =  5x + 2                             (multiplied both sides by 2)

-5x + 2y  =  2

5x - 2y  =  -2

Short way:     notice that the old equation   5x - 2y  =  6   and the new equation   5x - 2y  =  -2

have the same coefficients of the x-term and the y-term and their only difference is the constant.

So, to find the new equation, start with  5x - 2y  =

and put in the point (-2, -4) and solve:   5(-2) - 2(-4)  =  -10 + 8  =  -2

This will give us the new constant, so the new equation is  5x - 2y  =  -2

Apr 1, 2020