Question : The slope of the line passing through the points (2, –1) and ($x$, 5) is –1. Find $x$.
Option 1: 4
Option 2: –4
Option 3: –8
Option 4: 8
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Correct Answer: –4
Solution :
Given: The slope of the line passing through the points (2, –1) and ($x$, 5) is –1.
Slope($m$) of the line joining $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given by,
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$⇒ -1=\frac{5-(-1)}{x-2}=\frac{6}{x-2}$
$⇒ -x+2=6$
$⇒x=-4$
Hence, the correct answer is –4.
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