About This Chapter
Standard: Graph linear and quadratic functions and show intercepts, maxima, and minima. (CCSS.Math.Content.HSF-IF.C.7a)
Standard: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (CCSS.Math.Content.HSF-LE.A.2)
Standard: Interpret the parameters in a linear or exponential function in terms of a context. (CCSS.Math.Content.HSF-LE.B.5)
Standard: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. (CCSS.Math.Content.HSF-LE.A.1b)
About This Chapter
After students have a thorough understanding of linear functions, they'll be able to create functions and sequences and find the parameters in a function. Students will also be able to use the basics of linear equations to create a graph using a standard form or slope intercept.
Lessons for the standard include such topics as:
- What is a linear equation?
- Standard form, intercepts and graphing linear equations
- Abstract algebraic examples and going from a graph to a rule
- Graphing basic functions
- Graphing undefined slope, zero slope and more
- Finding the equation of a line from graphs, descriptions or points
- Interpreting the coefficients of a linear equation in context
- Lines as models for growth
- Real-world linear growth
You'll be able to tell when students fully comprehend linear functions when they are capable of graphing functions, locating line equations and using lines to show growth. The combination of lessons and standards can be a way for your students to prepare for higher education and several careers that employ this mathematical concept, such as computer programmer, surveyor, physicist or urban planner.
How to Use These Lessons in Your Classroom
Assign Lessons to Students
Rather than showing the lessons during class, you can assign them as homework and review the practice problems in class. By using a combination of the video lessons and your own lessons, students can get a more well-rounded education on linear functions.
Use Real Life Examples
To show students how useful linear functions are, show them how they can be used in day-to-day life or within specific situations, such as converting temperature or currencies. This will get students thinking about linear functions in new ways and might get them more excited about learning more.
Use Quizzes as Pre-Tests
To prepare students for the day's lesson, have them take the short quiz associated with the concept you'll be discussing. Have them re-take the quiz after you've taught the concept. Use the video lessons to illustrate points that might still cause some confusion.
1. What is a Linear Equation?
Most cars won't be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.
2. Abstract Algebraic Examples and Going from a Graph to a Rule
Just because you now know what a linear equation is doesn't mean that you are a master! This video will help you learn how to apply your knowledge of linear equations in more abstract algebraic ways.
3. Graphing Basic Functions
Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.
4. Graphing Undefined Slope, Zero Slope and More
There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the Common Core Math - Functions: High School Standards course
- Common Core HS Functions - Basics
- Common Core HS Functions - Sequences
- Common Core HS Functions - Graphing
- Common Core HS Functions - Quadratic Functions
- Common Core HS Functions - Common Functions & Transformations
- Common Core HS Functions - Polynomial Functions
- Common Core HS Functions - Rational Functions
- Common Core HS Functions - Exponential & Logarithmic Functions
- Common Core HS Functions - Trigonometric Functions