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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.
Solution
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
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