What is the area, in square units, of the interior region formed by the lines $y = 4x - 6, y = -2x +12$ and the $y$-axis?

Guest Jun 24, 2018

#2**+2 **

This region will form a triangle

To find the height of this triangle, let us fihd the x value of the intersection of the lines....set the y's equal

4x - 6 = -2x + 12 add 2x to both sides, add 6 to both sides

6x = 18 divide both sides by 6

x = 3 this x value will be the height of the triangle

And the y intercept of 4x - 6 = -6

And the y intercept of -2x + 12 = 12

So....the length of the base of this triangle = 12 - (-6) = 18

So....the area of the tiriangle is (1/2) (base length) (height) = (1/2)(18)(3) = 27 units^2

Here's a pic :

https://www.desmos.com/calculator/9svh83h2ij

CPhill Jun 25, 2018