Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.

From the graph find :

(i) the co-ordinates of the point where the two lines intersect;

(ii) the area of the triangle between the lines and the x-axis.

First equation: 6y = 5x + 10

Step 1:

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

Let x = -8, then 6y = 5 $\times$ (-8) + 10 ⇒ y = -5

Let x = -2, then 6y = 5 $\times$ (-2) + 10 ⇒ y = 0

Let x = 4, then 6y = 5 $\times$ 4 + 10 ⇒ y = 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: y = 5x - 15

Step 1:

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

Let x = 3, then y = 5 $\times$ 3 - 15 ⇒ y = 0

Let x = 4, then y = 5 $\times$ 4 - 15 ⇒ y = 5

Let x = 5, then y = 5 $\times$ 5 - 15 ⇒ y = 10

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.

(i) Both the straight line drawn meet at the point A. As it is clear from the graph, co-ordinates of the common point A are (4, 5).

Hence, the co-ordinates of the point where the two lines intersect = (4, 5).

(ii) The area of the triangle = $\dfrac{1}{2}$ x base x height

= $\dfrac{1}{2}$ x BC x AD

= $\dfrac{1}{2}$ x 5 x 5

= $\dfrac{25}{2}$ sq. units

= 12.5 sq. units

Hence, the area of the triangle between the lines and the x-axis = 12.5 sq. units.