Definition of Slope in Math

Introduction for definition of slope in math:

Definition:

The slope of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is

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

Source: Wikipedia

The definition of slope in math example problems and practice problems are given below.

Example Problems for Definition of Slope in Math:

Example problem 1:

Determine the slope of the line, 5x - y = -13

Solution:

The slope intercept form of a line is y = mx + b, where m is the slope of the line.

Given equation is in the form of ax + bx + c = 0. To find the slope of the line, we have to convert the equation from general form to slope intercept form.

The given equation can be converted from general form to slope intercept form as follows,

5x - y = -13

Subtract 5x on both sides,

5x - y - 5x = -13 - 5x

-y = -13 - 5x

Divide by (-1) on both sides.

`-y/(-1) ` = -`(13)/(-1)` - `(5x)/(-1)`

y = 13 + 5x

y = 5x + 13

Now the equation is in the form of y = mx + b, so the slope of the given line is 5

Example problem 2:

Determine the slope of a line, which contains the points A (4, -3), B (-2, 8).

Solution:

The slope of a line which contains two points (x1, y1) and (x2, y2) is given by,

Here, x1 = 4, x2 = -2, y1 = -3, y2 = 8.

Slope of the line, m = ` (y_2 - y_1)/(x_2 - x_1)`

m = `(8 + 3)/( -2 - 4)`

m = `-11/6`

Slope of the line (m) = `-11/6`

So, the slope of a line, which contains the points A (4, -3), B (-2, 8) is `-11/6`

Practice Problems for Definition of Slope in Math:

Practice problem 1:

Determine the slope of the line, 8x - y = -60

Answer: Slope (m) = 8

Practice problem 2:

Determine the slope of the given points: (12, -4) and (2, 8)

Answer: Slope (m) =  `-6/5`