# Finding a Slope of a Line Using 4 Methods

In this lesson, you will learn how to find a slope of a line using four different methods. But before that, perhaps here you will need to remember what we saw in Lesson "What is the Slope of a Line".

The slope of a line is the steepness of a line, or how quickly it rises (or falls) as we move from left to right. To measure this steepness, we define run to be the distance we move to the right, and rise to be the corresponding distance that the lines rises (or falls). The slope of a line is the ratio of rise and run:

The four ways to determine the slope of a line:

## Find the slope of the line from a table

To determine the slope of a line from a table.

Step 1: Identify the vertical change in each consecutive pair of y-values in the table.

Step 2: Identify the horizontal change in each consecutive pair of x-values in the table.

Step 3: Write ratios showing the corresponding in simplest form.

#### Example1:

Fin the slope of line from the table bellow:

Step 1: The change in each consecutive pair of y-values:

Step 2: The change in each consecutive pair of x-values:

Step 3: Write the ratios: .

The slope of the line is

## Find the slope of the line from a graph

To ind the slope of line from a graph:

Step 1: Pick any two points on the line. Get the coordinates of the two point and .

Step 2: Calculate the slope using the slope formula:

#### Example2:

Find the slope of a line in the graph below:

Step 1: Pick two different points in the graph (It is better to choose points whose coordinates are integers)

Step 2: In this case, and , Thus, the slope is:

## Find the slope of line passing through two points

To find the slope of a line passing through two points, it is sufficient to use only the slope of the line formula.

If the line passes through and , therefor, the slope is:

#### Example3:

Find the slope of a line passing through the two points and .

## Find the slope of the line from an equation

we use this method when we have the linear functions and the affine functions.

Step 1: Rewrite the equation in the form: .

Step 2: Slope is the rate of change, therefore, it's next to the variable . i.e, the slope is the coefficient of .

#### Example3:

Find the slope in each equation:

#### Solution:

Therefore, the slope is

Therefore, the slope is

Therefore, the slope is

Therefore, the slope is

Therefore, the slope is

In this case, we should isolate y of the equation.

We got

Therefore, the slope is