# 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