6.2 Formulas and Modeling 309 We will discuss the slope–intercept form of a line in detail in Section 6.6. Note that once you have found = − + y , x2 10 5 you have solved the equation for y. The solution can also be expressed in the form y x 2. 2 5 = − + This form of the equation is convenient for graphing equations, as will be explained in Section 6.6. Many formulas contain Greek letters, such as μ (mu), σ (sigma), Σ (capital sigma), δ (delta), Δ (capital delta), ε (epsilon), π (pi), θ (theta), and λ (lambda). Our next example involves Greek letter variables. Example 5 Standard Score Formula This example involves an important formula from statistics used to determine the standard score, or z-score. z x μ σ = − Solve this formula for x. Solution To isolate the term x, use the general procedure for solving linear equations given in Section 6.1. Treat each variable, except x, as if it were a constant. μ σ σ μ σ σ σ μ σ μ μ μ σ μ σ μ = − ⋅ = − ⋅ = − + = − + + = = + z x z x z x z x z x x z or Multiply both sides of the equation by σ. Add μ to both sides of the equation. 7 Now try Exercise 49 Learning Catalytics Keyword: Angel-SOM-6.2 (See Preface for additional details.) Example 6 The Slope–Intercept Form of the Equation of a Line A formula used to represent a linear equation, the slope–intercept form of the equation of a line, is y mx b = + Solve this equation for m. Solution To isolate the variable m, use the general procedure for solving linear equations given in Section 6.1. Treat each variable, except m, as if it were a constant. = + − = + − − = − = − = y mx b y b mx b b y b mx y b x mx x y b x m Subtract b from both sides of the equation. Divide both sides of the equation by x. 7 Now try Exercise 45 Instructor Resources for Section 6.2 in MyLab Math • Objective-Level Videos 6.2 • PowerPoint Lecture Slides 6.2 • MyLab Exercises and Assignments 6.2
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