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

3x + 4y = 24

$\dfrac{x}{4} + \dfrac{y}{3} = 1$

First equation = 3x + 4y = 24

Step 1:

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

Let x = -2, then 3 $\times$ (-2) + 4y = 24 ⇒ y = 7.5

Let x = 0, then 3 $\times$ 0 + 4y = 24 ⇒ y = 6

Let x = 2, then 3 $\times$ 2 + 4y = 24 ⇒ y = 4.5

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 = $\dfrac{x}{4} + \dfrac{y}{3} = 1$

Step 1:

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

Let x = -1, then $\dfrac{-1}{4} + \dfrac{y}{3} = 1$ ⇒ y = 3.7

Let x = 0, then $\dfrac{0}{4} + \dfrac{y}{3} = 1$ ⇒ y = 3

Let x = 1, then $\dfrac{1}{4} + \dfrac{y}{3} = 1$ ⇒ y = 2.2

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.