Q.5 (i) If the point (2, 1) lies on the graph of the equation \(x + ay = 4\), then find the value of ‘a’ and draw the graph of the equation so obtained.
Best answer
Answer: \(a = 2\); the graph is the straight line \(x + 2y = 4\) through (0, 2), (2, 1) and (4, 0)
Since (2, 1) lies on \(x + ay = 4\), it satisfies the equation: \(2 + a(1) = 4 \Rightarrow a = 2\).
The equation is \(x + 2y = 4\), i.e. \(y = \dfrac{4 - x}{2}\).
| \(x\) | 0 | 2 | 4 | –2 |
| \(y\) | 2 | 1 | 0 | 3 |
| \((x, y)\) | (0, 2) | (2, 1) | (4, 0) | (–2, 3) |
Graph (to be drawn on graph paper): Scale: on both axes 1 cm = 1 unit. Draw the X-axis and Y-axis through the origin O. Plot the points (–2, 3), (0, 2), (2, 1) and (4, 0) and join them with a straight line; extend it on both sides and label it \(x + 2y = 4\). The line cuts the Y-axis at (0, 2) and the X-axis at (4, 0), and passes through the given point (2, 1).
(Note: a picture of the graph cannot be shown here; in the examination the graph itself must be drawn as described above.)
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