Question

Draw the graphs of linear equations y = x and y = – x on the same cartesian plane. What do you observe?

Answer 1

The given equation is y = x. To draw the graph of this equation, we need at least two points lying on the given line.

For x = 1, y = 1, therefore (1, 1) satisfies the linear equation y = x.

For x = 4, y = 4, therefore (4, 4) satisfies the linear equation y = x.

By plotting the points (1, 1) and (4, 4) on the graph paper and joining them by a line, we obtain the graph of y = x.

The given equation is y = – x. To draw the graph of this equation, we need at least two points lying on the given line.

For x = 3, y = – 3, therefore, (3, – 3) satisfies the linear equation y = – x.

For x = – 4, y = 4, therefore, (– 4, 4) satisfies the linear equation y = – x.

By plotting the points (3, – 3) and (– 4, 4) on the graph paper and joining them by a line, we obtain the graph of y = – x.

We observe that, the line y = x and y = – x intersect at the point O(0, 0).