Draw the graph of the equation

4x + 3y + 6 = 0

From the graph, find :

(i) y₁, the value of y, when x = 12

(ii) y₂, the value of y, when x = -6

Step 1:

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

Let x = -3, then 4 $\times$ (-3) + 3y + 6 = 0 ⇒ y = 2

Let x = 0, then 4 $\times$ 0 + 3y + 6 = 0 ⇒ y = -2

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

Let x = 8, then 4 $\times$ 8 + 3y + 6 = 0 ⇒ y = -12.6

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 y₁, the value of y, when x = 12:

Through the point x = 12, draw a vertical straight line which meets the line AB at point C.

Through point C, draw a horizontal line which meets the y-axis at y = -18.

Hence, the value of y, when x = 12 is -18 , i.e, y₁ = -18.

(ii) To find y₂, the value of y, when x = -6:

Through the point x = -6, draw a vertical straight line which meets the line AB at point D.

Through point D, draw a horizontal line which meets the y-axis at y = 6.

Hence, the value of x, when y = -5 is 6, i.e, y₂ = 6.