SOLUTION: If a line intersects the x-axis at (a,0) and the y-axis at (0,b) at what point does it intersect the line y=x?
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Question 670835: If a line intersects the x-axis at (a,0) and the y-axis at (0,b) at what point does it intersect the line y=x?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If a line intersects the x-axis at (a,0) and the y-axis at (0,b) at what point does it intersect the line y=x?
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Equation of the line thru (a,0) and (0,b)
y/b + x/a = 1
y = x
----
Solve for x and y:
x/b + x/a = 1
----
ax + bx = ab
(a+b)x = ab
x = (ab)/(a+b)
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Since x = y, the point of intersection is (ab/(a+b) , ab/(a+b))
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The equation of the line through
(a,0) and (0,b) has slope =
and the y-intercept is
The equation is
And, since , the intersection is at
( (a*b)/( a-b ) , (a*b)/( a-b ) ) answer
-------------------------
check answer:
Suppose ,
and
OK
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