1. 3.8 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Rewrite Equations and Formulas

2. 3.8 Warm-Up ANSWER 2a + 3 = 24 1. Write an equation for “ 3 more than twice a is 24. ” ANSWER 64 ft 2 2.A square has a side length of 8 feet. Find the area of the square using the formula A = s 2.

3. 3.8 Warm-Up ANSWER 468 in. 2 3. A rectangular serving tray is 26 inches long and 18 inches wide. What is the tray’s serving area?

4. 3.8 Example 1 Subtract b from each side. Write original equation. Solve ax + b = c for x. STEP 1 SOLUTION Solve ax + b = c for x. Then use the solution to solve 2x + 5 = 11. x c – b a = ax + b = c ax = c – b Assume a  0. Divide each side by a.

5. 3.8 Example 1 The solution of 2x + 5 = 11 is 3. ANSWER Simplify. Substitute 2 for a, 5 for b, and 11 for c. Solution of literal equation. Use the solution to solve 2x + 5 = 11. STEP 2 11 – 5 2 = x = c – b a =3

6. 3.8 Guided Practice 1. a – bx = c ; 12 – 5x = –3 Solve the literal equation for x. Then use the solution to solve the specific equation ; 3 ANSWER x = a – c b 2. ax = bx + c ; 11x = 6x + 20 ; 4 ANSWER c x =x = a – ba – b

7. 3.8 Example 2 Divide each side by 2. Write original equation. Write 3x + 2y = 8 so that y is a function of x. Subtract 3x from each side. 3x + 2y = 8 2y2y = 8 – 3x 3 2 y=4 – x

8. 3.8 Guided Practice 3. Write 5x + 4y = 20 so that y is a function of x. 5 4 y=5 – x ANSWER

9. 3.8 Example 3 Multiply each side by 2. Write original formula. SOLUTION Use the rewritten formula to find the height of the triangle shown, which has an area of 64.4 square meters. b. Solve the formula for the height h. a. The area A of a triangle is given by the formula A = bh where b is the base and h is the height. 1 2 a. bh 1 2 A = 2A2A = Divide each side by b. 2A2A b h=

10. 3.8 Example 3 Substitute 64.4 for A and 14 for b. Write rewritten formula. Substitute 64.4 for A and 14 for b in the rewritten formula. b. = 2(64.4) 14 = 9.2 Simplify. ANSWERThe height of the triangle is 9.2 meters. h 2A2A b =

11. 3.8 Guided Practice The perimeter P of a rectangle is given by the formula P = 2l + 2w where l is the length and w is the width. a. Solve the formula for the width w. 4. w = or w = – l P – 2l 2 ANSWER P 2 2.4 ANSWER Use the rewritten formula to find the width of the rectangle shown. b.

12. 3.8 Example 4 You are visiting Toronto, Canada, over the weekend. A website gives the forecast shown. Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. Use the formula C = (F – 32) where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. 5 9 Temperature

13. 3.8 Example 4 Simplify. Write original formula. Multiply each side by, the reciprocal of. 9 5 5 9 Add 32 to each side. 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. (F – 32) 5 9 C= F – 32C 9 5 = 9 5 C + 32 = F · (F – 32) 9 5 5 9 C 9 5 = ANSWER 9 5 = Therewritten formula is F C + 32.

14. 3.8 Example 4 The low for Saturday is 57.2°F. ANSWER = 25.2 + 32 Saturday ( low of 14°C) Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. STEP 2 Sunday ( low of 10°C) = (14)+ 32 9 5 = (10)+ 32 9 5 = 18 + 32 = 57.2= 50 C + 32 9 5 F = F 9 5 = The low for Sunday is 50°F. ANSWER

15. 3.8 Guided Practice Use the information in Example 4 to find the high temperatures for Saturday and Sunday in degrees Fahrenheit. 5. 71.6°F, 60.8°F ANSWER

16. 3.8 Lesson Quiz 1. Write the equation 15 = 5y – 4x so that y is a function of x. y = x + 3 4 5 ANSWER 2. Solve C = 2  r for r. ANSWER r =  C 2 3. Solve V = Bh for B. 1 3 ANSWER B = 3V3V h

17. 3.8 Lesson Quiz 4.On a round-trip bicycle trip from Santa Barbara to Canada, Phil rode 2850 miles in 63 days. Find his average miles per day for the trip. Use the formula d = rt where d is distance, r is rate, and t is time. Solve for r to find the rate in miles per day to the nearest mile. about 45 miles per day ANSWER