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: $color(brown)(("change in y-axis")/("change in x-axis"))$

$color(white)(xxxxxx)color(brown)(= (y_2-y_1)/(x_2-x_1) )$

$color(blue)("You have "(x_1,y_1)-> (3/5,2))$

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

So $= (y_2-y_1)/(x_2-x_1) =(5/4 -2)/(2/10-3/5)$

$= (5/4 -8/4)/(1/5-3/5)$

$=(-3/4)/(-2/5)$

This is the same as $(-3/4) divide (-2/5)$

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

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

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

Or $( 15 divide 8 )/(8 divide 8) = (1.875)/1$

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