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Question
For the linear equation, given above, draw the graph and then use the graph drawn (in the following case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:
3x − (5 − y) = 7
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Solution
First draw the graph as follows:
Simplify the given equation
3x − (5 − y) = 7
3x − 5 + y = 7
3x + y = 12
To plot the graph, we need x-intercept and y-intercept.
When y = 0:
3x = 12 ⟹ x = 4
So, the x-intercept = (4, 0)
When x = 0:
y = 12
So, the y-intercept = (0, 12)
O(0, 0), A(4, 0), B(0, 12)
Area of triangle OAB:
Area `= 1/2` × base × height
Base = OA = 4 units
Height = OB = 12 units
Area `= 1/2` × 4 × 12
= 24
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