Question

Use graph paper and take 2 cm = 1 unit on both axes. Draw the graphs of x + y + 2 = 0 and 3x – 2y + 1 = 0. Write down the co-ordinates of the point of intersection of the lines.

Answer 1

1. Prepare for graphing

To draw the graphs, we first determine a few points for each line using the scale 2 cm = 1 unit. This means every 2 cm on your graph paper represents 1 whole number on the axes.

For the line x + y + 2 = 0 (y = –x – 2):

If x = 0, y = –2.

Point: (0, –2)

If x = –2, y = 0.

Point: (–2, 0)

If x = 2, y = –4.

Point: (2, –4)

For the line 3x – 2y + 1 = 0 (y = 1.5x + 0.5):

If x = 1, y = 2.

Point: (1, 2)

If x = –1, y = –1.

Point: (–1, –1)

If x = 3, y = 5.

Point: (3, 5)

2. Plot the lines

1. Draw the axes: Use a ruler to draw horizontal (x) and vertical (y) axes. Mark every 2 cm as 1, 2, 3 etc.

2. Plot the points: Mark the three points calculated for each line above on the grid.

3. Draw the lines: Use a straight edge to connect the points for each equation, extending them across the paper.

3. Find the intersection

By observing the graph, both lines cross at a single point. This point aligns with –1 on the x-axis and –1 on the y-axis.

The coordinates of the point of intersection are (–1, –1).