Determine $x$ , so that $2$ is the slope of the line through $(2, 5)$ and $(x, 3)$ .

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Solution

we know that slope of line passing through $(x_{1}, y_{2}), (x_{2}, y_{2}) = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

The slope of the line through $(2, 5)$ and $(x, 3)$ is $\frac{3 - 5}{x - 2}$ . But, the slope of the line is given as $2$ .

Therefore,

$\frac{3 - 5}{x - 2} = 2$

$2 x - 4 = - 2$

$x = 1$

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135^{\circ}

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