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?
+128470
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
