Modeling Linear Functions：模型的线性函数.ppt

MAC 1105 Module 2 Modeling Linear Functions Learning Objectives Upon completing this module, you should be able to: Recognize linear equations. Solve linear equations symbolically and graphically. Find the zeros of a function. Identify solutions, zeros, and x-intercept. Solve an equation for a specified variable. Learning Objectives Identify a table of values for a linear function. Use constant first differences. Model data with a linear function. Use linear regression to model data. Apply problem-solving strategies. Modeling Linear Functions 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 ≠ 0. (Note the power of x is always 1.) Examples of linear equations in one variable: 5x + 4 = 2 + 3x simplifies to 2x + 2 = 0 Note the power of x is always 1. ?1(x – 3) + 4(2x + 1) = 5 simplifies to 7x + 2 = 0 Note the power of x is always 1. Examples of equations in one variable which are not linear: x2 = 1 (Note the power of x is NOT 1.) (Note the power of x is NOT always 1.) How to Solve a Linear Equations Symbolically? Solve ?1(x – 3) + 4(2x + 1) = 5 for x ?1x + 3 + 8x + 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. How to Solve a Linear Equation Involving Fractions Symbolically? Solve Solution Process: How to Solve a Linear Equation Graphically? Solve Solution Process: Graph in a window in which the graphs intersect. How to Solve a Linear Equation Graphically?(Cont.) Locate points of intersection. x-coordinates of points o