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Find the gradient of the line passing through the points \((...

Find the gradient of the line passing through the points \((\frac{1}{2},  \frac{- 1}{3})  and  ( 3 , \frac{2}{3})\)

A.

\(\frac{2}{5}\)

B.

\(\frac{5}{2}\)

C.

\(\frac{2}{7}\)

D.

\(\frac{7}{2}\)

Correct answer is A

Gradient(slope) m = \(\frac{ y_2 - y_1}{ x_2 - x_1}\)

the points are  \((\frac{1}{2},  \frac{- 1}{3})  and  ( 3 , \frac{2}{3})\)

m = \(\frac{\frac{2}{3} - (\frac{-1}{3})}{3 - \frac{1}{2}}\)

=  \(\frac{\frac{2}{3} + \frac{1}{3}}{3 - \frac{1}{2}}\)

= \(1 \div\frac{5}{2}\) = \(1\times\frac{2}{5}\)           

Therefore, m = \(\frac{2}{5}\)