Solve for the slope and length of a line segment

[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?

 

[scurty]

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?

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.

Think about slope.

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.

 

[ehild]

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?

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. *.