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

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) (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 .

Since the area is 54,

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

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 .
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