The main contents of this chapter include all of the following: Functions, basic types of functions, constructing a table of signs, operations on functions, piecewise-defined functions, functions as mathematical models. | General Mathematics ADE 101 Unit 2 LECTURE No. 12 Liner Equations and Graph of Liner Equations Today’s Objectives Knowledge Test Draw the graph of the equation x+2=y What is a Linear Equation? A linear equation is an equation whose graph forms a straight line. Linear equations are usually shown on a coordinate plane Real life situations of linear equations include the stock market as well as the payments of a car. A linear equation in one variable is an equation which can be written in the form: ax + b = c for a, b, and c real numbers with a 0. Linear equations in one variable: 2x + 3 = 11 2(x 1) = 8 Not linear equations in one variable: 2x + 3y = 11 Two variables can be rewritten 2x + ( 2) = 8. x is squared. Variable in the denominator (x 1)2 = 8 can be rewritten x + 5 = 7. Linear Equation in One Variable 9 A solution of a linear equation in one variable is a real number which, when substituted for the variable in the equation, makes the equation true. Example: Is 3 a solution of 2x + 3 = 11? 2x + 3 = 11 2(3) + 3 = 11 6 + 3 = 11 Original equation Substitute 3 for x. False equation 3 is not a solution of 2x + 3 = 11. Example: Is 4 a solution of 2x + 3 = 11? 2x + 3 = 11 2(4) + 3 = 11 8 + 3 = 11 Original equation Substitute 4 for x. True equation 4 is a solution of 2x + 3 = 11. Example: Solution 10 Forms of Linear Equations The forms of linear equations are the formats in which the information is written in. These two forms are the most commonly used ways to write linear equations. 1. Slope Intercept Form: y=mx+b 2. Standard Form: Ax + By =C Standard form of a linear equations in one variable If the “y” is not all by itself, then we must first use the rules of algebra to isolate the “y” term. For example in the equation: 2y = 8x + 10 You will notice that in order to get “y” all by itself we have to divide both sides by 2. After you have done that, the equation becomes: Y = 4x + 5 Only then can we determine the slope (4), and the y-intercept (+5) m = -3, b | General Mathematics ADE 101 Unit 2 LECTURE No. 12 Liner Equations and Graph of Liner Equations Today’s Objectives Knowledge Test Draw the graph of the equation x+2=y What is a Linear Equation? A linear equation is an equation whose graph forms a straight line. Linear equations are usually shown on a coordinate plane Real life situations of linear equations include the stock market as well as the payments of a car. A linear equation in one variable is an equation which can be written in the form: ax + b = c for a, b, and c real numbers with a 0. Linear equations in one variable: 2x + 3 = 11 2(x 1) = 8 Not linear equations in one variable: 2x + 3y = 11 Two variables can be rewritten 2x + ( 2) = 8. x is squared. Variable in the denominator (x 1)2 = 8 can be rewritten x + 5 = 7. Linear Equation in One Variable 9 A solution of a linear equation in one variable is a real number which, when substituted for the variable in the equation, makes the equation true. Example: Is 3 a .
