Draw the graph of the equation

2x - 3y - 5 = 0

From the graph, find :

(i) x₁, the value of x, when y = 7

(ii) x₂, the value of x, when 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 2 $\times$ (-2) - 3y - 5 = 0 ⇒ y = -3

Let x = 0, then 2 $\times$ 0 - 3y - 5 = 0 ⇒ y = -1.6

Let x = 2, then 2 $\times$ 2 - 3y - 5 = 0 ⇒ y = -0.3

Let x = 5, then 2 $\times$ 5 - 3y - 5 = 0 ⇒ y = 1.6

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 AB passing through the points plotted on the graph.

(i) To find x₁, the value of x, when y = 7:

Through the point y = 7, draw a horizontal straight line which meets the line AB at point C.

Through point C, draw a vertical line which meets the x-axis at x = 13.

Hence, the value of x, when y = 7 is 13 , i.e, x₁ = 13.

(ii) To find x₂, the value of x, when y = -5:

Through the point y = -5, draw a horizontal straight line which meets the line AB at point D.

Through point D, draw a vertical line which meets the x - axis at x = -5.

Hence, the value of x, when y = -5 is -5, i.e, x₂ = -5.