How would you find the area of the region enclosed between the lines y equals -5x - 28 -4y plus 6x plus 18 equals 0 and the y axis?

y = -5x -28

-4y + 6x + 18 = 0 -> y = 3x/2 + 9/2

y-axis: x = 0

First, find the y-intercepts to determine 2 of the points of the triangle (substitute x=0 into the first two equations):

y = -28 (0, -28)

y = 9/2 (0, 9/2)

Then, find where the two equations intersect each other to determine the 3rd point of the triangle:

3x/2 + 9/2 = -5x - 28

3x + 9 = -10x - 56

13x = -65

x = -5, y = -3 (-5, -3)

From this, we know the height of the triangle is 5 (distance from y-axis to the 3rd point of the triangle), and the base of the triangle is 65/2 (the distance between the y-intercepts).

The area of the triangle is b*h/2 = 325/4