Question

Question 1
Draw the graph 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.
Observation
We observe that, the line y = x and y = -x intersect at origin (0,0).