ca_m2_handouts

ca_m2_handouts - MAC 1105 Module 2 Modeling Linear...

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1 Rev.S08 MAC 1105 Module 2 Modeling Linear Functions Rev.S08 2 Learning Objectives Upon completing this module, you should be able to: 1. Recognize linear equations. 2. Solve linear equations symbolically and graphically. 3. Find the zeros of a function. 4. Identify solutions, zeros, and x-intercept. 5. Solve an equation for a specified variable. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Rev.S08 3 Learning Objectives 6. Identify a table of values for a linear function. 7. Use constant first differences. 8. Model data with a linear function. 9. Use linear regression to model data. 10. Apply problem-solving strategies. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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2 Rev.S08 4 Modeling Linear Functions ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. - Algebraic and Graphical Solutions of Linear Equations - Fitting Lines to Data Points: Modeling Linear Functions There are two major topics in this module: Rev.S08 5 Linear Equations in One Variable A linear equation in one variable is an equation that can be written in the form ax + b = 0 where a and b are real numbers with a 㱠! 0. (Note the power of x is always 1.) Examples of linear equations in one variable: 5 x + 4 = 2 + 3 x simplifies to 2 x + 2 = 0 Note the power of x is always 1. 1( x – 3) + 4(2 x + 1) = 5 simplifies to 7 x + 2 = 0 Note the power of x is always 1. Examples of equations in one variable which are not linear: x 2 = 1 (Note the power of x is NOT 1.) (Note the power of x is NOT always 1.) ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Rev.S08 6 How to Solve a Linear Equations Symbolically? Solve 1( x – 3) + 4(2 x + 1) = 5 for x 1 x + 3 + 8 x + 4 = 5 7x + 7 = 5 7x = 5 – 7 7x = 2 x = 2/7 “Exact Solution” Linear Equations can always be solved symbolically and will produce an EXACT SOLUTION. The solution procedure is to isolate the variable on the left in a series of steps in which the same quantity is added to or subtracted from each side and/or each side is multiplied or divided by the same non-zero quantity. This is true because of the addition and multiplication properties of equality. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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3 Rev.S08 7 How to Solve a Linear Equation Involving Fractions Symbolically? Solve Solution Process: ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. When solving a linear equation involving fractions, it is often helpful to multiply both sides by the least common denominator of all of the denominators in the equation. The least common denominator of 3 and 4 is 12. Note that this is another “Exact Solution.” Rev.S08 8 How to Solve a Linear Equation Graphically? Solve Solution Process: Graph in a window in which the graphs intersect.
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ca_m2_handouts - MAC 1105 Module 2 Modeling Linear...

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