Question

What is the slope of the line passing through the following points: `(5, -6) , (2, 5)`?

Answer 1

`Slope = -11/3`

Explanation:

`color(blue)("Slope of a line (m)" = (y_1-y_2)/(x_1-x_2))`

Here , `color(red)(x_1=5)`

`color(red)(y_1=-6)`

`color(red)(x_2=2)`

`color(red)(y_2=5)`

Put these values in the slope equation

`=> color(magenta)(Slope = ((-6)-(5))/((5)-(2)))`

`=> color(magenta)(Slope = (-6-5)/(5-2))`

`=> color(green)(Slope = -11/3)`

Answer 2

Hey!
Algebra is gr8. In this case, what you would do is use the slope formula; `m = (y_2 - y_1)/ (x_2 - x_1)`.

Explanation:

`m = (y_2 - y_1)/(x_2 - x_1)`

Where m = slope, and each 'y' or 'x' term is inserted from your coordinate points!

(5, -6)(2, 5)

'5' is `x_1`
'-6' is `y_1`
'2' is `x_2`
'5' is `y_2`
(Respectively, if you haven't noticed :)

Plug them in!

`m=(5 - (-6))/(2 -5)`
(Remember, two negatives cancel out, so the top will be 5 + 6)

`m=(5+6)/(2-5)`
`m = 11/-3`

Your slope is `-11/3`!
Or approximately 3.67 (rounded)