If the slope of a line joining $A (2, x) B (- 3, 7)$ is $1$ then find $x$ .

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Solution

As we know that the slope of a line joining the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given as-
$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Therefore,
Slope of line joining the points $A (2, x)$ and $B (- 3, 7)$ is-
$m_{A B} = \frac{7 - x}{- 3 - 2} = 1 (Given)$
$\Rightarrow \frac{7 - x}{- 5} = 1$
$\Rightarrow 7 - x = - 5 \Rightarrow x = 7 + 5 = 12$

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