Draw the graph for the equation given below :

$\dfrac{1}{2}x + \dfrac{2}{3}y = 5$

Find the co-ordinates of the points where the graph (line) drawn meets the co-ordinate axes.

$\dfrac{1}{2}x + \dfrac{2}{3}y = 5$

Step 1:

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

Let x = -2, then $\dfrac{1}{2} \times (-2) + \dfrac{2}{3}y = 5 ⇒ y = \dfrac{6 \times 3}{2} = 9$

Let x = 0, then $\dfrac{1}{2} \times 0 + \dfrac{2}{3}y = 5 ⇒ y = \dfrac{15}{2} = 7.5$

Let x = 2, then $\dfrac{1}{2} \times 2 + \dfrac{2}{3}y = 5 ⇒ y = \dfrac{4 \times 3}{2} = 6$

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.