# How do you find the slope given (3/5,2) (2/10,5/4)?

Nov 16, 2015

1.875
See the explanation!

#### Explanation:

Slope or ' gradient ' is the amount of 'up' for 1 'along'.

So it is: $\textcolor{b r o w n}{\left(\text{change in y-axis")/("change in x-axis}\right)}$

$\textcolor{w h i t e}{\times \times \times} \textcolor{b r o w n}{= \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}}$

$\textcolor{b l u e}{\text{You have } \left({x}_{1} , {y}_{1}\right) \to \left(\frac{3}{5} , 2\right)}$

color(blue)("and "color(white)(xxxx)color(blue)((x_2,y_2)-> (2/10,5/4))

So $= \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{\frac{5}{4} - 2}{\frac{2}{10} - \frac{3}{5}}$

$= \frac{\frac{5}{4} - \frac{8}{4}}{\frac{1}{5} - \frac{3}{5}}$

$= \frac{- \frac{3}{4}}{- \frac{2}{5}}$

This is the same as $\left(- \frac{3}{4}\right) \div i \mathrm{de} \left(- \frac{2}{5}\right)$

Same as $\left(- \frac{3}{4}\right) \times \left(- \frac{5}{2}\right) = + \frac{15}{8}$

$\textcolor{red}{\text{Note that (negative) "divide" (negative) = (positive)}}$

So for every 8 along you go 15 up ...... ( the gradient)

Or $\frac{15 \div i \mathrm{de} 8}{8 \div i \mathrm{de} 8} = \frac{1.875}{1}$