Find the slope of a line passing through the following points:

$(i) (- 3, 2) a n d (1, 4) (i i) (a t_{1}^{2}, 2 a t_{1}) a n d (a t_{2}^{2}, 2 a t_{2}) (i i i) (3, - 5), a n d (1, 2)$

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Solution

$(i) (- 3, 2) a n d (1, 4) Slope of line = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{4 - 2}{1 - (- 3)} = \frac{2}{4} = \frac{1}{2} (i i) (a_{1}^{2}, 2 a t_{1}) a n d (a t_{2}^{2}, 2 a t_{2}) Slope of line \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{2 a t_{2} - 2 a t_{1}}{a t_{2}^{2} - a t_{1}^{2}} = \frac{2 a (t_{2} - t_{1})}{a (t_{2} - t_{1}) (t_{2} + t_{1})} = \frac{2}{t_{2} + t_{1}} (i i i) (3, - 5), a n d (1, 2) Slope of line = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{2 - (- 5)}{1 - 3} = \frac{7}{- 2} = \frac{- 7}{2}$

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Similar questions

(a t_{1}^{2}, 2 a t_{1}) and (a t_{2}^{2}, 2 a t_{2})

Find the slope of a line passing through the following points:

$(i) (- 3, 2) a n d (1, 4) (i i) (3, - 5), a n d (1, 2)$

(- 3, 2)

\frac{- 5}{3}

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