404 CHAPTER 6 Algebra, Graphs, and Functions Important Facts and Concepts Examples and Discussion Section 6.1 Order of Operations Properties Used to Solve Equations Addition property of equality If a b, = then a c b c. + = + Subtraction property of equality If a b, = then a c b c. − = − Multiplication property of equality If a b, = then ac bc c , 0. = ≠ Division property of equality If a b, = then a c b c c , 0. = ≠ Examples 1–2, pages 296–297 Examples 4–13, pages 298–302 Section 6.2 Evaluating a formula Solving for a variable in a formula Examples 1–3, pages 307–308 Examples 4– 6, pages 308–309 Section 6.3 Applications of Linear Equations Proportions If a b c d ad bc where b 0 and d 0 , then . ≠ ≠ = = Examples 1– 4, pages 314–316 Examples 5– 6, pages 317–318 Section 6.4 Variation Direct: y kx = Inverse: y k x = Joint: y kxz = Examples 1–9, pages 322–327 Section 6.5 Inequality Symbols a b < means that a is less than b. a b ≤ means that a is less than or equal to b. a b > means that a is greater than b. a b ≥ means that a is greater than or equal to b. Examples 1–9, pages 331–334 Section 6.6 Intercepts To determine the x-intercept, set y 0 = and solve the resulting equation for x. To determine the y-intercept, set x 0 = and solve the resulting equation for y. Slope Slope = − − m m y y x x ( ): 2 1 2 1 Linear equation in two variables: ax by c a , 0 + = ≠ and b 0 ≠ Slope–intercept form of a line: y mx b = + Example 4, pages 342–343 Example 5, page 344–345 Examples 3, 4, 6, 7, 10, 11, pages 341–347 Examples 6–8, pages 345–346 Summary CHAPTER 6
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