Question

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

Answer 1

1.875
See the explanation!

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")`