Slope Formulas | List of Slope Formulas You Should Know - BYJUS

# Slope Formulas

In coordinate geometry or Euclidean geometry, the slope of a line in a two-dimensional plane can be determined by using the coordinates of two points in that plane. In this article, we are going to discuss how to calculate the slope of a line using two points lying on the same line on a coordinate plane....Read MoreRead Less

### What is the Slope Formula?

Slope of a line can be defined as the value of ratio of change in y (the rise) to the change in x (the run) between any two points of a line $$(x_1,~y_1)$$ and $$(x_2,~y_2)$$. The slope of a line can also be defined as the measurement of the steepness of that line. The slope of a line is generally denoted by ‘m’.

Slope, m = $$= [latex\frac{Change~in~y}{Change~in~x}$$

= 

### Types of Slope

Positive Slope: A line with a positive slope rises from left to right.

Negative Slope: A line with a negative slope rises from right to left.

Zero slope: A horizontal line has zero slope.

Undefined slope: The slope of a vertical line is ‘undefined’ or ‘not defined’.

### Solved Examples

Example 1: Find the slope of a line passing through the points (3, 7) and (5, 9).

Solution:

Slope, m = $$= \($$y_2\), -1 for $$y_1$$, 4 for $$x_2$$ and 7 for $$x_1$$

= $$Simplify = -[latex\frac{9}{3}$$

= – 3

Hence, the slope of the given line is – 3 (Negative slope).

Example 3:

After observing the graph of a line, Rhea realized that the rise of the graph is 12 units and the run is 4 units. Find the slope of Rhea’s line?

Solution:

Given that, Rise = 12 units

Run = 4 units.

Slope, m = $$m = [latex\frac{12}{4}$$ = 3.

Hence, the slope of the line is 3

Improper fractions are fractions that have  numerators that are greater than or equal to the denominators. For example: $$\frac{23}{5},\frac{13}{11},\frac{7}{2},\frac{6}{6}$$ and so on.
Mixed numbers are numbers between two whole numbers. So mixed numbers have a whole number part and a proper fraction. For example, $$1\frac{2}{3}$$ is a mixed number. This number lies between the wholes, 1 and 2. In $$1\frac{2}{3}$$, 1 is the whole number and $$\frac{2}{3}$$ is the proper fraction.
A proper fraction has the numerator lesser than the denominator. For example, $$\frac{1}{2},\frac{3}{4},\frac{11}{13}$$ and so on.