Final answer:
The area of the triangle formed by the line 3x - 4y = 12 and the x-axis and y-axis is 6 square units.
Step-by-step explanation:
The equation of the line is 3x - 4y = 12. To find the x-intercept (P), we substitute y = 0 into the equation and solve for x: 3x - 4(0) = 12. This simplifies to 3x = 12, and dividing both sides by 3 gives x = 4.
To find the y-intercept (Q), we substitute x = 0 into the equation and solve for y: 3(0) - 4y = 12. This simplifies to -4y = 12, and dividing both sides by -4 gives y = -3.
The area of the triangle formed by the x-axis, y-axis, and the line is given by |(x1 - x3)(y2 - y3)|/2. Using the x and y-intercepts, we have |(4 - 0)(-3 - 0)|/2 = |4(-3)|/2 = |-12|/2 = 6 square units.