## The Lesson

The slope of a line is its steepness. It is how far up a line goes compared to how far across it goes. The line below has a slope of**2**because it goes up 2 units for every 1 unit it goes across. A line can be represented by a linear equation. We can find the slope from a linear equation.

## How to Find the Slope from a Linear Equation in General Form

A linear equation (in general form) is given in the form below: The**a**,

**b**and

**c**do not immediately tell you anything about the line (such as its slope or y-intercept). But it can be converted to a form which does tell you about the line. For example, the slope-intercept form gives the slope and y-intercept. It is the

**m**in the slope-intercept form that tells you the slope. Once we know the slope-intercept form, we can read off the number in front of the

**x**(the

**m**) to find the slope. We can use algebra to convert the general form into the slope-intercept form: Comparing this with

**y = mx + c**, we see that the slope is

**−**. Read more about converting a linear equation in general form to slope-intercept form

^{a}⁄_{b}## A Real Example of Finding the Slope from a Linear Equation in General Form

Finding the slope of a line from a linear equation in general form is easy.## Question

Find the slope of the line given by the linear equation shown below.## Step-by-Step:

# 1

Find the number in front of the

**x**. In our example, the number in front of the x is**4**.**4**x + 2y + 2 = 0

# 2

Find the number in front of the

**y**. In our example, the number in front of the y is**2**.
4x +

**2**y + 2 = 0# 3

# 4

## Answer:

The slope is**−2**.

## More Examples of Finding the Slope of a Line from Linear Equations

All of the linear equations we have seen in this lesson have been in general form (**ax + b + c = 0**). There are other forms of linear equation. You must be able to find the y-intercept in all forms of linear equation.

- You need to be able to find the slope of a linear equation in slope-intercept form: Read more about finding the slope from a linear equation in slope-intercept form
- You need to be able to find the slope of a linear equation in slope-point form: Read more about finding the slope from a linear equation in slope-point form