SOLUTION: A triangle AOB is enclosed by a line, which cuts the y-axis at A and x-axis at B and the x and y-axes. If the line has a gradient of-0.75, and the triangle has an area of 54 unit^2

Algebra ->  Linear-equations -> SOLUTION: A triangle AOB is enclosed by a line, which cuts the y-axis at A and x-axis at B and the x and y-axes. If the line has a gradient of-0.75, and the triangle has an area of 54 unit^2      Log On


   

Question 1110393: A triangle AOB is enclosed by a line, which cuts the y-axis at A and x-axis at B and the x and y-axes. If the line has a gradient of-0.75, and the triangle has an area of 54 unit^2,
a). draw a diagram showing this information, and
b). find the equation of the line(s).
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


It is not specified in the statement of the problem, but I will assume the triangular region is in quadrant I. There is a second, corresponding solution with the region in quadrant III.

With the gradient of -3/4, we can let A = 4x and B = 3x.

Then the area of the triangle is %281%2F2%29%284x%29%283x%29+=+6x%5E2.

Since the area is 54,
6x%5E2+=+54
x%5E2+=+9
x+=+3

Then A is 4x=12 and B is 3x=9.

Now we have the gradient and the y-intercept; the equation of the line is y+=+%28-3%2F4%29x%2B12

The other solution comes from choosing x = -3 instead of x = 3 when solving x^2=9. The result is A = -12 and B = -9; the equation of the line is y+=+%28-3%2F4%29x-12.