- Find the equation of the line that passes through \((2,1)\) and \((-3,4)\). (2 marks)
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- Determine whether \((7,-2)\) lies on the line. (1 mark)
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a. \(y=\dfrac{4-1}{-3-2}=-\dfrac{3}{5}\)
b. \(\text {Substitute}\ (7,-2) \ \text{into equation:}\)
| \(-2\) | \(=-\dfrac{3}{5} \times 7+\dfrac{11}{5}\) |
| \(-2\) | \(=-\dfrac{21}{5}+\dfrac{11}{5}\) |
| \(-2\) | \(=-2 \ \text{(correct)}\) |
\(\therefore (7,-2) \text{ lies on line.}\)
a. \((2,1),(-3,4)\)
\(\text{Gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-1}{-3-2}=-\dfrac{3}{5}\)
\(\text{Find equation with} \ \ m=-\dfrac{3}{5} \ \ \text{through}\ \ (2,1):\)
| \(y-1\) | \(=-\dfrac{3}{5}(x-2)\) |
| \(y\) | \(=-\dfrac{3}{5} x+\dfrac{11}{5}\) |
b. \(\text {Substitute}\ (7,-2)\ \text{into equation:}\)
| \(-2\) | \(=-\dfrac{3}{5} \times 7+\dfrac{11}{5}\) |
| \(-2\) | \(=-\dfrac{21}{5}+\dfrac{11}{5}\) |
| \(-2\) | \(=-2 \ \text{(correct)}\) |
\(\therefore (7,-2) \text{ lies on line.}\)