SOLUTION: What are all the equations of the lines that intersect the graph of 5x+Y=14 at (2,4). Explain why.

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Question 1109058: What are all the equations of the lines that intersect the graph of 5x+Y=14 at (2,4).
Explain why.

Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that your given point IS on your given line.

5%2A2%2B1%2A4=14
You could use the coefficients as variables temporarily.
A%2A2%2BB%2A4=14
2A%2B4B=14

This is a line, with variable coefficients A and B, as if an ordered pair (A, B). As long as (A, B) is not (5,1), Any point (A,B) which satisfies line 2A+4B=14 will intersect 5x%2By=14.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What are all the equations of the lines that intersect the graph of 5x+Y=14 at (2,4).
Explain why.
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m = (4-y)/(2-x) = (y-4)/(x-2)
m*(x-2) = y-4
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Pick any value for m and it passes thru the point.
There are an infinite # of them.
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The equation shown is not relevant, it's one possible line.