IM3 - Lesson 5: Forms of Equations for Linear Functions Unit 1 Basics of Functions
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1 A. Lesson Contet BIG PICTURE of this UNIT: CONTEXT of this LESSON: What is meant by the term FUNCTIONS and how do we work with them? mastery with working with basics & applications of linear functions mastery with working with basics & applications of linear systems understanding basics of function concepts and apply them to lines & linear systems Where we ve been Where we are Where we are heading In Lessons 1-4, you practiced with basic concepts related to functions Connecting to Linear Relations, we now look at different forms of equations that describe linear functions. How do we apply the concept of functions to linear & eponential relations. B. Lesson Objectives a. Use an algebraic & graphic perspective to review fundamental skills (slope, intercepts, convert, evaluate & solve) related to slope-intercept & point-slope forms of linear equations b. Introduce standard form & intercept form of linear equations & relate back foundational skills c. Generate the graphs of these linear functions on technology (TI-84 & DESMOS) C. Fast Five (Skills Review Focus) 1. Write the equation of a line that passes through (-1,4) and has a slope of ½. 3. Sketch the function defined by the equation - + 5y = 0. Write the equation of a line that is parallel to the line y = 1 and passes through the point (8,-3) 4. The points (1,1) and (3,9) are points on the parent function y =. Determine the equation of the secant line through these two points. Illustrate with a diagram.
2 D. Observation Table for Eploration on Forms of Linear Equations (A) slope-intercept form or Function Form or General Form y = m + b f() = m + b Working with the equation f() = 3: (c) determine the -intercept of the line Working with the equation f() = 3: (d) evaluate f() (e) solve f() = 3 (f) rewrite equation in slope-point form EXAMPLE y = - 3 Include key points & labels & window settings
3 E. Observation Table for Eploration on Forms of Linear Equations (B) point-slope form Working with equation y 3 1 ( ): Working with equation y 3 1 ( ) (d) evaluate f() y y 1 = m( 1) also known as transformational form (e) solve f() = 6 f() y 1 = m( 1) f() = m( 1) + y 1 (c) determine the -intercept of the line (f) convert to function form EXAMPLE: y 3 1 ( ) Include key points & labels & window settings
4 F. Observation Table for Eploration on Forms of Linear Equations (C) standard form A + By = C Or A + By + C = 0 also known as implicit form Working with equation 5 4y 60: Working with the equation 5 4y 60: (d) evaluate f() (e) solve f() = 6 EXAMPLE: 5 4y 60 (c) determine the -intercept of the line (f) convert to function form (g) convert to point-slope form Include key points & labels & window settings
5 G. Observation Table for Eploration on Forms of Linear Equations (D) intercept form a y b 1 Working with equation 3 y 4 1 Working with the equation (e) evaluate f() 3 y 4 1 EXAMPLE: 3 y 4 1 (f) solve f() = 6 (c) determine the -intercept of the line (g) convert to point-slope form (d) convert to function form (h) convert to standard form Include key points & labels & window settings
6 H. CONSOLIDATION on Forms of Linear Equations (a) Rewrite the linear equation 4 y 1 = 0 in slopeintercept, slope-point & intercept forms (b) A line has a slope of 3 and has an -intercept at -5. Write the equation in all four forms. (c) Given the graph of the following line, write the equation in all four forms. (d) A line passes through the points A(-,5) and B(5,-1). Write the equation in all four forms. (e) Write the equation of the perpendicular bisector of the line segment connecting A(-1,3) and B(3,9). Write the equation in all four forms.
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