## The Slope-Intercept Form of an Equation

## Introduction

Consider the line that is drawn to the left. One way to describe it with an equation is to figure out the slope and the y-intercept of the line. These two pieces of information (the slope and the y-intercept) allow you to write the equation of the line. Since the equation describes the slope and the y-intercept of the line, is said to be written in slope-intercept form.

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.

## Lesson

Any linear equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept. This equation is a simple way to compare the x and y values of any line on the coordinate plane.

The two equations below are in slope-intercept form. Compare the two equations to their corresponding graphs to get an idea of how the slope and position of the line changes based on the slope and y-intercept in the equation.

When a line is written in slope-intercept form, it is possible to graph the line by starting at the y-intercept and then using the slope value to find other points to the right and left.

**Example 1****:** Draw the graph of the line y = 3x – 5

Solution:

Step 1: The y-intercept is -5, so plot the point (0, -5)

Step 2: The slope is 3, so add a second point by moving up 3 units and right 1 unit. The second point is (1, -2)

Step 3: Plot a third point by moving up 3 units and right 1 unit from the second point. The third point is (2, 1).

Step 4: Draw a line though the points.

Drawing three points is a good idea because you will draw a more accurate line than you would with only two points. Plotting three separate points gives your line better definition and ensures that you have not made a math error. If the three points are not collinear, then and check each coordinate again.

**Example 2:** Draw the graph of the line

Solution:

Step 1: The y-intercept is 1, so plot the point (0, 1)

Step 2: The slope is 2/3, so add a second point by moving up 2 units and right 3 units. The second point is (3, 3)

Step 3: Plot a third point by moving up 2 units and right 3 units from the second point. The third point is (6, 5).

Step 4: Draw a line though the points.

**Slope-Intercept Equations and T-Charts**

The examples that we have looked at so far compare the slope-intercept equation with the corresponding graph of a line. The one piece of information that was not included was the t-chart of the line. A t-chart is simply a chart that is used to list a number of coordinates of an equation. These coordinates can then be used to draw the graph of the equation.

Consider the equation y = -2x + 5. This equation can be compared to the t-chart and graph as follows:

The slope of this line is -2 and the y-intercept is the coordinate (0, 5). The three red -2’s next to the t-chart come from the slope of the equation. Since the slope is -2, the y-value decreases by 2 when the x-value goes up by 1.

## Try It

Find the slope and y-intercept for each equation:

1) y = x + 5

2) y = 4x + 6

3) y = -½x + 5

4) y = -6x

5) y = -2

Find the equation of each line below:

6)

7)

Scroll down for answers…

**Answers****:**

** **1) Slope is 1 and y-intercept is 5 (Equation: y = x + 5)

2) Slope is 4 and y-intercept is 6 (Equation: y = 4x + 6)

3) Slope is -½ and y-intercept is 5 (Equation: y = -½x + 5)

4) Slope is -6 and y-intercept is 0 (Equation: y = -6x or y = -6x + 0)

5) Slope is 0 and y-intercept is -2 (Equation: y = -2)

6)

7)

**Related Links: **

For more information on slope-intercept form and related topics, try one of the links below.

**Resource Pages**

- Graphing Linear Equations (Intro) Resource Page
- Graphing Linear Equations (Advanced) Resource Page

**Related Lessons**

- The Slope of a Line

- Changing an Equation into Slope-Intercept Form

- Find the Equation (Given 1 point and slope)

Looking for something else? Try the general math or algebra lesson links.