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

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) (Show Source): You can put this solution on YOUR website!
Notice that your given point IS on your given line.

You could use the coefficients as variables temporarily.

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 .
Answer by Alan3354(69443) (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.

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