SOLUTION: Find an equation for the given line in the form ax+by=​c, where​ a, b, and c are integers with no factor common to all three and a≥0. Through ​(minus&#8722

Algebra ->  Linear-equations -> SOLUTION: Find an equation for the given line in the form ax+by=​c, where​ a, b, and c are integers with no factor common to all three and a≥0. Through ​(minus&#8722      Log On


   

Question 1109538: Find an equation for the given line in the form ax+by=​c, where​ a, b, and c are integers with no factor common to all three and a≥0.
Through ​(minus−8​,12​); parallel to 3 x plus 2 y equals 17
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
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Through ​(minus−8​,12​); parallel to 3 x plus 2 y equals 17
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You can start with point-slope form.
Given equation is 3x%2B2y=17; so slope of this is -3%2F2.

You want, first, the equation y-12=-%283%2F2%29%28x-%28-8%29%29
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y-12=-3x%2F2-%283%2A8%29%2F2
y-12=-3x%2F2-12
y=-3x%2F2
3x%2F2%2By=0
highlight%283x%2B2y=0%29

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


If it is parallel to 3x+2y=17, then it is in the form 3x+2y=k for some constant k.

To find the value of k, use the fact that the coordinates of the given point satisfy the equation:
3%28-8%29%2B2%2812%29+=+k
-24%2B24+=+k
k+=+0

The equation is 3x+2y=0.