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 =

The area of the triangle is 18.70 sq.units.

Step-by-step explanation:

It is provided that a triangle is bounded by the y-axis, the line .

The slope of the line is:

A perpendicular line passes through the origin to the line f (x).

The slope of this perpendicular line is:

The equation of perpendicular line passing through origin is:

Compute the intersecting point between the lines as follows:

The value of y is:

The intersecting point is .

The y-intercept of the line f (x) is, 9, i.e. the point is (0, 9).

So, the triangle is  bounded by the points:

(0, 0), (0, 9) and

Consider the diagram attached.

Compute the area of the triangle as follows:

Thus, the area of the triangle is 18.70 sq.units.