How do you find a standard form equation for the line with P= (-5,-5) and Q= (-3,-2)?

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How do you find a standard form equation for the line with P= (-5,-5) and Q= (-3,-2)?

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Answer 1 · 2017-02-05T13:36:44

$3 x - 2 y = - 5$ $3x-2y=-5$
(see below for method)

Explanation:

Step 1: Develop a slope-point form for the line
The slope of a line between two points is defined as:
$XX$ $color(white)("XX")$ The difference between the $y$ $y$ coordinate values
$XX$ $color(white)("XX")$ divided by the corresponding difference between the $x$ $x$ coordinates.
$color(white)("XXXXX")m=(Deltay)/(Deltax)= (-2-(-5))/(-3-(-5))=3/2$

This relationship must hold for any arbitrary point $(x,y)$ on the line;
so
$color(white)("XXXXX")m=(y-(-5))/(x-(-5))=(y+5)/(x+5)$

Therefore
$color(white)("XXXXX")(y+5)/(x+5)=3/2$
or
$color(white)("XXXXX")y+5 =3/2(x+5)$

Step 2: Convert the slope-point form into standard form
Note that the standard form for a linear equation is
$color(white)("XX")Ax+By=C$ with constants $A, B, C$ and $A>=0$

If
$color(white)("XXXXX")y+5=3/2(x+5)$
then
$color(white)("XXXXX")2(y+5)=3(x+5)$
$rArr$
$color(white)("XXXXX")2y+10=3x+15$
$rArr$
$color(white)("XXXXX")-5=3x-2y$
or
$color(white)("XXXXX")3x-2y=-5$

Here is the graph for verification purposes:
enter image source here

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How do you find a standard form equation for the line with P= (-5,-5) and Q= (-3,-2)?

1 Answer

Explanation:

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