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

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Answer 1 · 2015-11-16T20:29:32

1.875
See the explanation!

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

So it is: $\frac{change in y-axis}{change in x-axis}$ $color(brown)(("change in y-axis")/("change in x-axis"))$

$\times \times \times = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $color(white)(xxxxxx)color(brown)(= (y_2-y_1)/(x_2-x_1) )$

$You have (x_{1}, y_{1}) \to (\frac{3}{5}, 2)$ $color(blue)("You have "(x_1,y_1)-> (3/5,2))$

$and \times \times (x_{2}, y_{2}) \to (\frac{2}{10}, \frac{5}{4})$ $color(blue)("and "color(white)(xxxx)color(blue)((x_2,y_2)-> (2/10,5/4))$

So $= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{\frac{5}{4} - 2}{\frac{2}{10} - \frac{3}{5}}$ $= (y_2-y_1)/(x_2-x_1) =(5/4 -2)/(2/10-3/5)$

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

$= \frac{- \frac{3}{4}}{- \frac{2}{5}}$ $=(-3/4)/(-2/5)$

This is the same as $(- \frac{3}{4}) \div (- \frac{2}{5})$ $(-3/4) divide (-2/5)$

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

$Note that (negative) \div (negative) = (positive)$ $color(red)("Note that (negative) "divide" (negative) = (positive)")$

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

Or $\frac{15 \div 8}{8 \div 8} = \frac{1.875}{1}$ $( 15 divide 8 )/(8 divide 8) = (1.875)/1$

$For every 1 along you go up 1.875$ $color(green)("For every 1 along you go up 1.875")$