For the pair of linear equations given below, draw graphs and then state, whether the lines drawn are parallel or perpendicular to each other.

y = x - 3
y = - x + 5

First equation = y = x - 3

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then y = (-1) - 3 ⇒ y = - 4

Let x = 0, then y = 0 - 3 ⇒ y = - 3

Let x = 1, then y = 1 - 3 ⇒ y = - 2

Let x = 4, then y = 4 - 3 ⇒ y = 1

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second equation = y = - x + 5

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then y = - (-1) + 5 ⇒ y = 6

Let x = 0, then y = - 0 + 5 ⇒ y = 5

Let x = 1, then y = - 1 + 5 ⇒ y = 4

Let x = 4, then y = - 4 + 5 ⇒ y = 1

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Hence, the two lines are perpendicular to each other.