Question

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 coordinates of the point where the two lines intersect;
(ii) the area of the triangle between the lines and the x-axis.

Answer 1

6y = 5x + 10
⇒ y = `(5x + 10)/(6)`
The table of 6y = 5x + 10 is

X	4	- 2	- 8
Y	5	0	- 5

Also, we have
y = 5x - 15
The table of y = 5x - 15 is

X	3	4	5
Y	0	5	10

Plotting the points in a graph, we get the following graph.

(i)
The two lines intersect at (4, 5)
∴ AD ⊥ BC
AD = 5 units and BC = 5 units

(ii)

The area of the triangles = `(1)/(2) xx "BC" xx "AD"`

= `(1)/(2) xx 5 xx 5`

= `(25)/(2) "sq.units"`

= 12.5 sq.units