SOLUTION: Find an equation for each line in the form ax+by=c, where a,b,c are integers with no factor common to all three and a >_0. Question: Through (2,-5), parallel to 2x-y=-4

Question 755679: Find an equation for each line in the form ax+by=c, where a,b,c are integers with no factor common to all three and a >_0.
Question: Through (2,-5), parallel to 2x-y=-4
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Parallel lines have equal slopes. First, determine the slope of the line comprised of the set of ordered pairs that is the solution set of the given equation. The easiest way to do this is to solve the equation for

in terms of

and examine the coefficient on

that results.

Now that you have the slope of the desired line and a point on the desired line, use the point-slope form of an equation of a line to derive a form of the required equation:

where

are the coordinates of the given point and

is the calculated slope.

Once you have substituted the available values, rearrange the equation into the required form, namely

where

and

, by ordinary algebraic means, i.e. adding the same quantity to both sides of the equation or multiplying both sides of the equation by the same quantity.

John

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