# 4.5: Graphs Using Slope-Intercept Form

Difficulty Level:

**At Grade**Created by: CK-12Turn In

## Learning Objectives

At the end of this lesson, students will be able to:

- Identify the slope and \begin{align*}y-\end{align*}intercept of equations and graphs.
- Graph an equation in slope-intercept form.
- Understand what happens when you change the slope or intercept of a line.
- Identify parallel lines from their equations.

## Vocabulary

Terms introduced in this lesson:

- slope-intercept form
- rise
- run
- parallel lines

## Teaching Strategies and Tips

Use Examples 1 and 2 to make observations such as:

- \begin{align*}m < 0\end{align*} when a line slants downward and \begin{align*}m > 0\end{align*} when it slants upward.
- \begin{align*}m = 0\end{align*} when a line is horizontal.
- \begin{align*}b < 0\end{align*} when the \begin{align*}y-\end{align*}intercept is below the \begin{align*}x-\end{align*}axis and \begin{align*}b > 0\end{align*} when it’s above the \begin{align*}x-\end{align*}axis.
- \begin{align*}b = 0\end{align*} when a line passes through the origin.

Use the slope-intercept method to graph lines as an alternative to plotting and joining two intercepts.

With a graphing utility, demonstrate the effects on a line when changing \begin{align*}m\end{align*} and \begin{align*}b\end{align*} one at a time in an equation in slope-intercept form. Make observations such as:

- The larger the \begin{align*}m\end{align*}, the steeper the line.
- Negative slopes can also represent steep lines. The smaller the \begin{align*}m\end{align*} (more negative), the steeper the line.
- Slopes approximately equal to zero represent lines that are almost horizontal.
- Changing the intercept shifts a line up/down.
- Parallel lines have the same slope but different \begin{align*}y-\end{align*}intercepts.

## Error Troubleshooting

In Example 2, use the marked lattice points and/or intercepts in the slope calculation for each line. Using these points allows students to obtain exact answers. See also *Review Questions*, Problems 2 and 3.

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
---|---|---|---|

Show More |

### Image Attributions

Show
Hide
Details

Description

No description available here...

Tags:

Activities
Answer Key
Answers
(55 more)
arithmetic progression
Assessment
axes
CK.MAT.ENG.TE.1.Algebra-I.4
coefficient
common difference
Common Misconceptions
Concept Check and Troubleshooting
constant of proportionality
continuous function
coordinate plane
Differentiated Instruction
direct variation
discrete function
domain
Enrichment
Equation
Function
graphs of equations
graphs of functions
Inquiry Process
intercept
linear functions
Newton's 2nd Law
Ohm's Law
Ordered Pair
ordinate
Origin
Pacing
Problem Sets
Problem Solving
Quadrant
Quizzes
range
rate of change
relation
rise over run
Science Inquiry
slope
slope-intercept form
Solution Key
Solutions
standard form
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
velocity
vertical line test
Worksheets
x-axis
x-coordinate
y-axis
y-coordinate

Subjects:

Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
Files can only be attached to the latest version of section