Find the area of a triangle bounded by the y-axis, the line f(x) = 9 − 6/7 x, and the line perpendicular to f(x) that passes through the origin. (Round your answer to two decimal places.)

Answer 1

y = 7x/6, x= 0 and y = 9-6x/7

enclose a triangle. what is it's area??

height = 9

area = hb/2 = 9b/2

b = distance from x =0 to x coordinate of where y=9-6x/7 and y=7x/6 intersect

7x/6 = 9-6x/7

7x/6 +6x/7 = 9

49x +36x = 9(42)

x = 9(42)/85 =

area = 9(9(42)/85)/2 = 81(21)/85 = about 20.01176 square units

= 20.01 units^2 rounded to 2 decimal places