Question

The equation y – 6 = m (x – 3) represents a line. For what value(s) of m does this line form a triangle with the positive axes of area 48?

Answer 1

@mathmale

Answer 2

@DanJS

Answer 3

@skullpatrol

Answer 4

If you're familiar with the "point-slope" form of the equation of a straight line, you know that (h,k) represents a point on the line; in your case, that point is (3,6).

I'd suggest you sketch this situation.

Suppose we first assume that there is only one value of m for which the triangle formed by this line and the positive x- and y-axes has an area of 48 square units.

If that's the case, then the formula for the area of that triangle is \[\frac{ 1 }{ 2 }bh\]

Answer 5

where b is the length of the base of the triangle and h is the height. In this case, "h" would be "y" and both would represent the height of the triangle.

You were given y-6=m(x-3). Solving for y, y=6+m(x-3). This could be simplified.

Then the area is (1/2) b h = (1/2)*x*(expression for y).

This area is 48 square units.

Unfortunately, you still have 2 variables: m and x.

So we'll need to determine whether there are other constraints. For example, the height of the triangle has the same numeric value as does the y-coordinate of the y-intercept.

I haven't taken this solution all the way to the end. Hope that the above remarks and suggestions give you something helpful to work from.

Answer 6

Note: If we arbitrarily choose m=-1, then the line has x-intercept (9,0) and y-intercept (0,9). The area of the resultant triangle is (1/2)bh, or (1/2)(9)(9)= (81/2) = 40.5 (too small).
Therefore, m=-1 won't "work."
You could try m=-1.2 and/or m=-0.8 and determine the area of the resulting triangle.

Good luck! Have fun!