What would the equation be?

Question

A triangular region in the first quadrant is formed by the coordinate axes and a line with negative slope, as sketched below Given that the xintercept is 9 and the triangle area is 9 square units, find an equation of the line .in y=mxtb form

Answer 1

y = mx + b; 0 = 9m + b and 9b/2 = 9; b = 2 and m = - 2/9

y = - 2/9x + 2

Answer 2

Know definitions: triangle, first quadrant, coordinate axes, negative slope, x-intercept (the place where y=0)

Know formulas: Area of triangle is (1/2)*base*height

Know Process: Given base and area, find height. Then, with slope and y-intercept, write equation of line in slope-intercept form (that is, y = mx+b). Note that b = height.

Area = 9 = (1/2)*9*height

height = b = 2

The y-intercept (the place where x=0) is the point (0,2). Note that this is b=2.

The slope, m, is -2/9

Since the y-intercept (b) is given, we may now write the equation in y=mx+b form:

y = -(2/9)x + 2