help im stuck on my hw assingment its precalculus

Question

Find the area of a triangle bounded by the  axis, the line , and the line perpendicular to  that passes through the origin.Area = 

Answer 1

y=(-4/7)x + 6 has slope = -4/7

the perpendicular line has slope with negative inverse or 7/4

y= (7/4)x is the equation of the perpendicular through the origin.

they intersect at (168/65, 294/65) = about (2.5846, 4.52308)

use the distance formula to calculate the distance to the origin and to the y intercept

that gives roughly sides of a right triangle = 5.21 and 2.98 with hypotenuse = 6

Area = (1/2)(5.21)(2.98) = 7.76

Answer 2

Need to find the height and the base of the triangle so you can use:

Area, A = (1/2) base×height

The line perpendicular to f(x) and passes through the origin is g(x) = 7x/4

The x-value of the intercept between these two line is

6-4x/7 = 7x/4

x = 168/65

If you plot these two lines you will see that the base of the triangle is between the y intercept of f(0) = 6 and the origin. The height of the triangle is the x-value of the intercept between the two lines.

A = (1/2)(168/65)(6) = 504/65