1.4 Finding Linear Functions
Contents
Objectives:[edit]
- Review and use the slope-intercept and point-slope forms for a line
- Use different forms of a line to find the formula of a linear function that is represented by a table, graph, set of points, etc.
- Definitions
- slope-intercept form, point-slope form
Lesson Guide[edit]
Have students do Problems 1 and 2.
- Once most of the students have finished problems 1 and 2 you should give a very short statement to the whole class to tie the warm-up together with the rest of what you will be covering. Something like "In problem 1 and problem 2 we used one important characteristic of a linear equation, what was that characteristic?" Allow students to share answers then ask "what is the other component of a linear equation?" Wait for responses. "Now I want you to use this to help you solve problem 3."
Review and use the slope-intercept and point-slope forms for a linear equation[edit]
Have students do Problem 3.
This may feel odd, why are we having students find the formula when we have not shown them how to do so. The vast majority of students actually know how to find the formula. We are pushing them to discover a formula on their own. Pay attention to what they do and use their ideas to help guide your lecture for the rest of the day.
Ask specific students to provide their solutions and how they got them. Ask for various methods students used on these Problems until someone offers ``slope-intercept form" and ``point-slope form" as strategies.
The slope-intercept form of a linear equation with slope Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} -intercept Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (0,b)} is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = mx+b. } A point-slope form of a linear equation with slope Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} and a point Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_0,y_0)} on the line is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y - y_0 = m(x-x_0) }
Use different forms of a line to find the formula of a linear function that is represented by a table, graph, set of points, etc.[edit]
Have students do Problems 4-7.
Have students write their answers on the board and make sure that the answers cover examples where you find the formula for a linear function given a graph, a set of points, or a word problem. You may want to show how to do such a problem given a table. In particular, you could go back to previous examples in the course packet (\S1.3) and use these tables and graphs now.
Once students have mastered the more basic Problems (5-7) have them move onto Problems 8. Be careful not to give away too much information early on in the semester.
End class by having a student present their answer to Problem 8. Tell students to talk about Problem 8 and make sure everyone at their table can master Problem 8. Problem 8 often comes up on either quizzes or exams.
Remember
- Students may need some reminder that they can find the slope using the formula.
- Students will likely struggle with finding the slope. Just remind them that they should know the formula for slope as well as the "rise over run" notion for slope, especially on the second graph.
- Students may have a difficult time determining which is the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} -value and which is the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} -value.
- Students will likely struggle with the idea that they need to solve for the unknown values.
Comments[edit]
In this area, you should feel free to add any comments you may have on how this lesson has gone or what other instructors should be aware of.
