B = 12/5 units
We can find the intersection point between these two lines:
y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
Add 2x to both sides of the equation.
2x = 8
Divide both sides of the equation by 2.
x = 4
Formula for the Area of a Triangle:
B = 1/2bh
Substitute 2 for b and 14/5 for h.
B = (1/2) · (2) · (12/5)
Multiply and simplify.
B = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
I hope this helps! o(〃＾▽＾〃)o