Find the area of a triangle bounded by the y-axis, the line f(x) = 4−5/7x, and the line perpendicular to f(x) that passes through the origin. (round your answer to two decimal places.)

The area of triangle is

Step-by-step explanation:

we have

The slope of the given linear function is

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

Find the slope of the line perpendicular to the given linear function

we have

substitute

Find the equation of the line perpendicular to the given linear function that passes through the origin

The line represent a direct variation, because the line passes through the origin

The equation is

Find the area of triangle bounded by the y-axis, the line f(x) = 4−5/7x, and the line perpendicular to f(x) that passes through the origin

using a graphing tool

see the attached figure

The vertices of the triangle are

A(0,0),B(1.892,2.649),C((0,4)

The area of the right triangle ABC is

the formula to calculate the distance between two points is equal to

Find the distance AB

Find the distance BC

Find the area of the right triangle ABC