# 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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 Click here to see ALL problems on Linear Algebra 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(69061)   (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? ------- 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) ----- Since x = y, the point of intersection is (ab/(a+b) , ab/(a+b)) ======================= Cheers, Stan H. ======================= Answer by josmiceli(13716)   (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