SOLUTION: A triangle AOB is enclosed by a line, which cuts the y-axis at A and the x-axis at B and the x and y axes. If the line has a gradient of -0.75, and the triangles has an area of 54

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A triangle AOB is enclosed by a line, which cuts the y-axis at A and the x-axis at B and the x and y axes. If the line has a gradient of -0.75, and the triangles has an area of 54       Log On


   

Question 1110307: A triangle AOB is enclosed by a line, which cuts the y-axis at A and the x-axis at B and the x and y axes. If the line has a gradient of -0.75, and the triangles has an area of 54 units squared.
find the equation of the line
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
This is what I have for the setup:

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+Area+=+%281%2F2%29A%2AB+=+54+ —> +AB=108+ (1)
y=mx+b (b=A by inspection, m=-0.75) —> y=-0.75x+A
(2) —> 0 = -0.75B+A —> A=0.75B (2)
Substitute 0.75B (from (2)) into (1):
++%280.75B%29B+=+108++
+++B%5E2+=+144+
++B+=+12+ —> +A+=+9+
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Ans: The line has equation +highlight%28+y=-0.75x+%2B+9%29+
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Check:
Area = (1/2)(9)(12) = 54 sq units (ok)
A is at (0,9), B is at (12,0) so slope = m = (9-0)/(0-12) = -(9/12) = -0.75 (ok)