Draw the graph of equation $\dfrac{x}{4} + \dfrac{y}{5} = 1$. Use the graph drawn to find :

(i) x₁, the value of x, when y = 10

(ii) y₁, the value of y, when x = 8.

Step 1:

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

Let x = -4, then $\dfrac{-4}{4} + \dfrac{y}{5} = 1$ ⇒ y = 10

Let x = 0, then $\dfrac{0}{4} + \dfrac{y}{5} = 1$ ⇒ y = 5

Let x = 4, then $\dfrac{4}{4} + \dfrac{y}{5} = 1$ ⇒ y = 0

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 = 10:

Through the point y = 10, 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 = -4.

Hence, the value of x, when y = 10 is -4 , i.e, x₁ = -4.

(ii) To find y₁, the value of y, when x = 8:

Through the point x = 8, draw a vertical line which meets the line AB at point D.

Now, through point D, draw a horizontal line which meets the y-axis at y = -5.

Hence, the value of y, when x = 8 is -5 , i.e, y₁ = -5.