Question : The slope of the line passing through the point (7, –2) and ($x$, 1) is $-\frac{3}{10}$. Find $x$.
Option 1: 4
Option 2: 2
Option 3: –4
Option 4: –3
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Correct Answer: –3
Solution :
Given: Slope of the line passing through points (7, –2) and ($x$, 1) is $\frac{–3}{10}$.
Slope of the line joining $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given by,
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$⇒\frac{-3}{10}=\frac{1-(-2)}{x-7}$
$⇒\frac{-3}{10}=\frac{3}{x-7}$
$⇒–3x+21=30$
$⇒–3x=9$
$⇒x=–3$
Hence, the correct answer is –3.
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