Question

What is the slope of the line between (6,9) and (18, -2 )?

Answer 1

The gradient is `color(white)(xx)color(blue)(-11/12)`.

As it is a negative slope it shows that it's gradient is downwards as you move from left to right.

Explanation:

Put in simple terms: It is the amount of 'up or down' for one along.

Let the gradient (slope) be m

Note the positive gradient is an upwards slope whilst a negative gradient is a downward one.

`m=("change in vertical")/("change in horizontal") -> (y_2-y_1)/(x_2-x_1)`

The negative 2 has been highlighted in blue. Subtracting or adding negative numbers needs a bit more care!
`(x_1 , y_1) ->( 6,9)`
`(x_2,y_2)->(18,color(blue)(-2))`

`m=(color(blue)(-2)-9)/(18-6)`

`m= -11/12`

It is more precise to keep this as a fraction.