What is the Slope Formula

There are a few concepts that come along with the slope concept like intercept form and point slope formula. Again the concept intercept form includes x and y intercept. Finding slope is done with the help of the point slope formula. Thus all these topics are interrelated.

The slope of a line means the steepness or incline of the line. The higher the slope value the more is the steeper incline.The slope of a line including the x axis and y axis is represented by m and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

The slope formula of the line is:

Slope (m) = [ (y2 - y1)/(x2 - x1)]

Slope (m) = $\frac{Rise}{Run}$

(Rise = change in the y co-ordinate; Run = change in the x co-ordinate)

In the above given graph, the Rise is given for the points B (4,2) and C (4,4) and the Run is given for the points A (2,2) and B (4,2)

Rise = change in the y - coordinate = 4-2 =2

Run = change in the x- coordinate = 4-2 =2

Using the slope formula, we get :

Slope( m ) = $\frac{Rise}{Run}$ = $\frac{2}{2}$ =1

Determine the slope of a line, which contains the points A (-1, -2), B (-2, 1):

Solution:

Here, x1 = -1, x2 = -2, y1 = -2, y2 = 1.

Slope of the line, m = [ $\frac{(y2 - y1)}{(x2 - x1)}$]

= [$\frac{(1 + 2)}{(-2 + 1)}$]

= [$\frac{3}{(-1)}$]

Slope of the line (m) = -3

Here are few other slope formula examples worked out for you with explanations

Problem 1:

Find the slope of the equation y=4x-3

Solution:

Y = 4x - 3

It is in the slope form y = mx + b.

So, slope(m) = 4

Problem 2:

Find the slope of the equation 3y = 6x - 12

Solution:

3y = 6x - 12

Divide by 3 on both sides,

Y = 2x - 4

So, slope(m) = 2

Work out these problems and get a clear understanding of finding the slope of a line. If you find any difficulties, just connect to our expert online tutor and thus gain quality information from the comfort of your home.