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)=6-1/5x, the line perpendicular to f(x) that passes through the origin.

Area= _______

Answer 1

f(x) = 6 - (1/5)x

has a perpendicular line with a negative inverse slope = 5

y=5x is perpendicular and through the origin, having zero y intercept

f(x) = y = 6 -x/5 has intercept =6

the y axis is x=0

set 6-x/5 = 5x

solve for x

6=5x + x/5

6= 26x/5

26x = 6(5)

13x=15

x = 15/13 = height of the triangle

6 = base

height times base divided by 2 = area of the triangle

(15/13)6/2 = area = 45/13 = 3 6/13