The slope of a line is equal to the change in y divided by the change in x, or

`(Deltay)/(Deltax)`

For a line `y=ax+b` the slope is equal to a.

Example:

`y=3x+1` , a=3

Pick two points on the line: (0,1) and (1,4)

`(Deltay)/(Deltax)=(4-1)/(1-0)=3`

The slope is equal to** a=3**

To find the slope of a line means to find the rate of change between any two given points.

Therefore if we know one point has coordinates `(x_(1), y_(1)) and`

another point has coordinates `(x_(2), y_(2))` then we can find the rate of change by finding `(Deltay)/(Deltax).`

`(Deltay)/(Deltax) = (y_(2)-y_(1))/(x_(2)-x_(1))`

For example, if a line had points (2, -3) and (-1, 5) to find the slope we perform the following calculations.

`(5 - (-3))/(-1 - 2)` = `8/-3`

Therefore, the slope of this line would be `-8/3.`