Solve for the slope and length of a line segment

1. Dec 28, 2013

Husaaved

The problem is to a.) solve for the slope m of the hypotenuse of the right triangle indicated by the shaded area, and b.) solve for the length of the hypotenuse, if possible. I made a mistake in transcribing the problem onto paper, the line of course extends indefinitely but the shaded area and the length of the line bounded by the y- and x-axes are all that are of interest.

The area of the shaded area is 4, and a single point along the line are all that is given. I get also that a (0, y) and (x, 0) are also given, and I know that the point-slope formula is y - y1 = m(x - x1, but I'm not sure in what way to apply this information to the problem.

Any thoughts?

2. Dec 28, 2013

scurty

There are two pieces of information given, the area and a point on the line. A good starting point would be to write down the area in terms of a formula. $A=\frac{1}{2}bh$.

You have two unknowns, so you need another equation so you can substitute variables to solve for the other.

Edit: That might have been too vague. How can you relate x and y together using slope? Then use that relationship in the area formula to solve for x and y.

Last edited: Dec 28, 2013
3. Dec 28, 2013

ehild

You know x1=2 and y1=1. Plug in these data into the formula y-y1=m(x-x1) *

Denote the X-intercept by a and the Y intercept by b. How do you get the shaded area in terms of a and b?

You get equations for a and b in terms of m by substituting (a,0) and (0,b) into eq. *.