Question

How do you find the slope of (1,5), (-8,2)?

Answer 1

Slope = `1/3`

Explanation:

To find the slope for any 2 points `(x_1,y_1) and (x_2, y_2)`, you use the following formula:

slope formula: `m = [y_1 - y_2] / [x_1 - x_2]`

For our case, points are (1,5) and (-8,2)

slope `m = (5-2)/(1-(-8))` = `3/9 = 1/3`

Answer 2

The gradient (slope) is `1/3`

Explanation:

Like the gradient on a hill, the slope (gradient) is the amount of change in the up or down for the given amount of along as you read from left to right.

Let the gradient be `m`

`m=("change in up or down")/("change in along")->("change in y")/("change in x")`

I have reversed the order of your points so that the `x` values read left to right.

Let the first point be `" "P_1->(x_1,y_1)=(color(brown)(-8,2))`
Let the second point be `P_2->(x_2,y_2)=(color(blue)(1,5))`

`m=(color(blue)(y_2)color(brown)(-y_1))/(color(blue)(x_2)color(brown)(-x_1)) = color(brown)(color(blue)(5)-2)/(color(blue)(1)color(brown)(-(-8)))`

But `1-(-8)` is the same as `1+8`
Note that 2 minuses is the same as a plus.

`m=(5-2)/(1+8)=3/9`

But `3/9-=(3-:3)/(9-:3)-=1/3`

So the gradient (slope) is `1/3`

This means that if you move to the right by 3 you have gone up 1
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Additional Teaching bit")`
Suppose the gradient had been `-1/3`

This would mean that you go to the right by 3 but you go down 1.

Negative gradient is a downward slope ( left to right)
Positive gradient is an upward slop (left to right)