Find the area of a triangle bounded by the y axis

Question

Find the area of a triangle bounded by the y axis, the line f(x)=9−2/3x, and the line perpendicular to f(x) that passes through the origin.

Area =   ______

Answer 1

9-2x/3 = 3x/2

3x/2 + 2x/3 = 9

9x/6 + 4x/6 = 9

13x/6 = 9

13x =54

x = 54/13

use 9 as the base, 54/13 as the height

Area = bh/2

Area = (54/13)9/2 = 27(9)/13 = 243/13 = 18 9/13