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3-7 HW: Pg. 179-181 #6-18eoe, 20-28e, 33-35, 41-42 41. C 42. C Wir2.5 • LESSON 3-8 Rewrite Equations and Formulas Function Form: an equation in x and y written so the dependent variable y is isolated on one side of the equation. - SOLVE FOR y - function of y in terms of x Literal Equation: an equation that contains 2 or more variables EXAMPLE 1 Solve a literal equation Solve ax + b = c for x. Then use the solution to solve 2x + 5=11. STEP 1 Solve ax + b = c for x. Write original equation. ax + b = c –b - b Subtract b from each side. ax = c – b Assume a 0. Divide each side by a. a a c–b x= a c–b Solution of literal equation. x = a 11 – 5 Substitute 2 for a, 5 for b, and 11 for c. = 2 Simplify. =3 SOLUTION STEP 2 ANSWER The solution of 2x + 5 = 11 is 3. GUIDED PRACTICE for Example 1 Solve the literal equation for x. Then use the solution to solve the specific equation 1. a – bx = c; 12 – 5x = –3 2. ax = bx + c; 11x = 6x + 20 ANSWER a–c x = b ;3 ANSWER c x= ;4 a–b EXAMPLE 2 Rewrite an equation Write 3x + 2y = 8 so that y is a function of x. 3x + 2y = 8 – 3x - 3x 2y = 8 – 3x 2 2 y = 4 – 3x 2 Write original equation. Subtract 3x from each side. Divide each side by 2. EXAMPLE 3 Solve and use a geometric formula 1 The area A of a triangle is given by the formula A = bh 2 where b is the base and h is the height. a. Solve the formula for the height h. Use the rewritten formula to find the height of the triangle shown, which has an area of 64.4 square meters. 1 SOLUTION Write original formula. a. A = 2 bh 2A = bh Multiply each side by 2. 2A =h Divide each side by b. b b. Substitute 64.4 for A and 14 for b in the rewritten formula. 2A h= b Write rewritten formula. 2(64.4) = 9.2 Substitute 64.4 for A and 14 for b. Simplify. = 14 The height of the triangle is 9.2 meters. ANSWER b. GUIDED PRACTICE for Examples 2 and 3 Write 5x + 4y = 20 so that y is a function of x. 5 ANSWER y = 5 – x 4 4 . The perimeter P of a rectangle is given by the formula P = 2l + 2w where l is the length and w is the width. 3. a. Solve the formula for the width w. P – 2l P w= or w = –l ANSWER 2 2 b . Use the rewritten formula to find the width of the rectangle shown. ANSWER 2.4 EXAMPLE 4 Solve a multi-step problem Temperature You are visiting Toronto, Canada, over the weekend. A website gives the forecast shown. Find the low temperatures for Saturday and Sunday in degrees 5 Fahrenheit. Use the formula C = (F – 32) where C is 9 the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Rewrite the formula. In the problem, degrees Celsius are given and degrees Fahrenheit need to be calculated. The calculations will be easier if the formula is written so that F is a function of C. 5 C = 9 (F – 32) Write original formula. 9 9 5 9 C = · (F – 32) Multiply each 5side by 5, the 5 9 reciprocal of . 5 9 9 C = F – 32 Simplify. 5 9 C + 32 = F Add 32 to each side. 5 ANSWER The rewritten formula is F = 9 C + 32. 5 EXAMPLE 4 STEP 2 Solve a multi-step problem Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. Saturday (low of 14°C) 9 F = C + 32 5 9 = 5 (14)+ 32 Sunday (low of 10°C) 9 F = C + 32 5 9 = 5 (10)+ 32 = 25.2 + 32 = 18 + 32 = 57.2 = 50 ANSWER ANSWER The low for Saturday is 57.2°F. The low for Sunday is 50°F. GUIDED PRACTICE for Example 4 5. Use the information in Example 4 to find the high temperatures for Saturday and Sunday in degrees Fahrenheit. ANSWER 71.6°F, 60.8°F Summary • How do you rewrite equations? • Ans: Use inverse operations to get the needed variable alone on one side. • Describe and correct the error in the following problem: Solve the equation for x: ax b 0 ax b b x a • Ans: You need to subtract b to move it to the other side, so ax = -b, so the answer is x = -b/a Check Yourself Pg. 187-189 #4-22e, 28, 32, 38-39 and Quiz on Pg. 189 #1-8