Question

The graph of 3x + 2y = 12 meets the x-axis at point P and the y-axis at point Q. Use the graphical method, to find the co-ordinates of points P and Q.

Answer 1

Step 1: Find the coordinates of point P (x-intercept)

To find where the graph meets the x-axis, we set y = 0 in the equation:

3x + 2(0) = 12

3x = 12

`x = 12/3`

x = 4

Thus, the coordinates of point P are (4, 0).

Step 2: Find the coordinates of point Q (y-intercept)

To find where the graph meets the y-axis, we set x = 0 in the equation:

3(0) + 2y = 12

2y = 12

`y = 12/2`

y = 6

Thus, the coordinates of point Q are (0, 6).

Step 3: Graphical method

By plotting these two points, P(4, 0) and Q(0, 6), on a Cartesian plane and drawing a straight line through them, we represent the equation 3x + 2y = 12. The points where this line intersects the axes are precisely our calculated values.