Question

What is the slope between `(-3 , 3)` and `(5, 11)`?

Answer 1

`"slope "=1`

Explanation:

`"calculate the slope using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-3,3)" and "(x_2,y_2)=(5,11)`

`m=(11-3)/(5-(-3))=8/8=1`

Answer 2

The slope of the line between `(-3,3)` and `(5,11)` is `1`.

Explanation:

To calculate the slope/gradient of a linear function when we are given two coordinate points on the line, we can use the formula for linear gradient:

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

Essentially, this formula gives us the ratio between the change in `y` and the change in `x` between the two coordinates.

mathisfun.com

So, this formula accounts for two sets of coordinates, `(x_1, y_1)` and `(x_2, y_2)`. We simply need to substitute your points into these:

`(-3, 3) -> (x_1, y_1)`
`(5, 11) -> (x_2, y_2)`

Hence:

`x_1 = -3`
`x_2 = 5`
`y_1 = 3`
`y_2 = 11`

Now, we substitute these into the formula and simplify:

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

`=(11-3)/(5-(-3))`

`=(11-3)/(5+3)`

`=(8)/(8)`

`=1`