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 = 3x - 1
y = 3x + 2

First equation = y = 3x - 1

Step 1:

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

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

Let x = 0, then y = 3 $\times$ 0 - 1 ⇒ y = -1

Let x = 1, then y = 3 $\times$ 1 - 1 ⇒ y = 2

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 = 3x + 2

Step 1:

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

Let x = -2, then y = 3 $\times$ (-2) + 2 ⇒ y = -4

Let x = -1, then y = 3 $\times$ (-1) + 2 ⇒ y = -1

Let x = 0, then y = 3 $\times$ 0 + 2 ⇒ y = 2

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 parallel to each other.