Question : A slope of line AB is $-\frac{2}{3}$. Co-ordinates of points A and B are $(x,–3)$ and $(5, 2)$, respectively. What is the value of $x$?
Option 1: 4
Option 2: –14
Option 3: 12.5
Option 4: –4
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Correct Answer: 12.5
Solution :
Given: A slope of line AB is $-\frac{2}{3}$. Co-ordinates of points A and B are $(x,–3)$ and $(5, 2)$, respectively.
Slope of line(m) $=\frac{y_{2}–y_{1}}{x_{2}–x_{1}}$
$⇒-\frac{2}{3}= \frac{2–(–3)}{5–x}$
$⇒-\frac{2}{3}= \frac{2+3}{5–x}$
$⇒-\frac{2}{3}= \frac{5}{5–x}$
$⇒-10+2x=15$
$\therefore x=12.5$
Hence, the correct answer is 12.5.
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