1. Warm Up

2. Lesson 1.5 – Rewriting Equations and Formulas
Today’s Learning Goal is: Students will be able to rewrite literal equations, rewrite and use formulas for area and use other common formulas.

3. Core Vocabulary
Literal Equation – an equation that has two or more variables
Formula – A literal equation that shows how one variable is related to one or more other variables

4. 1 Examples Solve 3y + 4x = 9 for y. 3y + 4x = 9 Write the Equation
3y+4x -4x=9-4x Subtract 4x from both side of =
3y = 9 – 4x Simplify
Divide by 3
𝑦= 9 3 − 4𝑥 Simplify
𝑦=3− 4𝑥 Simplify 1

5. Examples
2. Solve the literal equation y=3x + 5xz for x. y = 3x + 5xz Write the Equation y = x(3 + 5z) Distributive Property (3 + 5z) (3 + 5z) Divide by (3 + 5z) y = x Simplify (3 + 5z) 1

6. You Try! Solve for y 3y – x = 9 3y –x +x =9 +x 3y = 9 + x 3 3
𝑦= 𝑥 3
𝑦=3+ 𝑥 3

7. You Try! Solve for y 2. 2x – 2y = 5 2x – 2x – 2y = 5 – 2x -2y = 5 – 2x
𝑦= 5 −2 − 2𝑥 −2
𝑦=− 5 2 +𝑥

8. You Try! Solve for y 3. 20 = 8x + 4y 20 -8x = 8x – 8x + 4y
20 4 − 8𝑥 4 = 4𝑦 4
5−2𝑥=𝑦

9. You Try!

10. Examples
3. The formula for the surface area S of a rectangular prism is S = 2ℓw + 2ℓh + 2wh. Solve the formula for the length ℓ.
SOLUTION
S = 2ℓw + 2ℓh + 2wh Write the equation.
S − 2wh = 2ℓw + 2ℓh + 2wh − 2wh Subtract 2wh from each side.
S − 2wh = 2ℓw + 2ℓh Simplify.
S − 2wh = ℓ(2w + 2h) Distributive Property
𝑆 − 2𝑤ℎ 2𝑤 + 2ℎ = ℓ(2w + 2h) 2w + 2h Divide each side by 2w + 2h.
S − 2wh 2w + 2h = ℓ Simplify.

11. A =ℓw Write the formula for area of a rectangle.
4. You own a rectangular lot that is 500 feet deep. It has an area of 100,000 square feet. To pay for a new water system, you are assessed $5.50 per foot of lot frontage. a. Find the frontage of your lot. b. How much are you assessed for the new water system?
SOLUTION
In the formula for the area of a rectangle, let the width w represent the lot frontage.
A =ℓw Write the formula for area of a rectangle.
𝐴 𝑙 = w Divide each side by ℓ to solve for w.
100, = w Substitute 100,000 for A and 500 for ℓ.
200 = w Simplify.
The frontage of your lot is 200 feet.
b. Each foot of frontage costs $5.50, and $5.50/1 ft ⋅ 200 ft = $1100. So, your total assessment is $1100.

12. You Try!

13. Core Concepts
Common Formulas Temperature F= degrees Fahrenheit, C= degrees Celsius C= 𝟓 𝟗 (F-32) Simple Interest I= interest, P= principal r= annual interest rate (decimal form) t= time (years) I=Prt
In notebook- do not need to write down

14. Core Concepts
Common Formulas Distance d= distance traveled r= rate t = time d=rt
In notebook- do not need to write down

15. Examples
5. Solve the temperature formula for F. SOLUTION C = 5 9 (F − 32) Write the temperature formula. 9 5 C = F − 32 Multiply each side by C + 32 = F − Add 32 to each side. 9 5 C + 32 = F Simplify. The rewritten formula is F = 9 5 C + 32.

16. 6. Which has the greater surface temperature: Mercury or Venus
6. Which has the greater surface temperature: Mercury or Venus? SOLUTION Convert the Celsius temperature of Mercury to degrees Fahrenheit. F = 9 5 C + 32 Write the rewritten formula from Example 5. = 9 5 (427) + 32 Substitute 427 for C. = Simplify. Because 864°F is greater than 800.6°F, Venus has the greater surface temperature.

17. I = Prt Write the simple interest formula.
7. You deposit $5000 in an account that earns simple interest. After 6 months, the account earns $ in interest. What is the annual interest rate?
SOLUTION
To find the annual interest rate, solve the simple interest formula for r.
I = Prt Write the simple interest formula.
I Pt = r Divide each side by Pt to solve for r.
(5000)(0.5) = r Substitute for I, 5000 for P,
and 0.5 for t.
0.065 = r Simplify.
The annual interest rate is 0.065, or 6.5%.

18. 8. A truck driver averages 60 miles per hour while delivering freight to a customer. On the return trip, the driver averages 50 miles per hour due to construction. The total driving time is 6.6 hours. How long does each trip take?
SOLUTION
Step 1 Rewrite the Distance Formula to write expressions that represent the two trip times. Solving the formula d = rt for t, you obtain t = 𝑑 𝑟 . So, 𝑑 60 represents the delivery time, and 𝑑 50 represents the return trip time.

19. Step 2 Use these expressions and the total driving time to write and solve an equation to find the distance one way. 𝑑 60 + 𝑑 50 = 6.6 The sum of the two trip times is 6.6 hours. 11𝑑 300 = 6.6 Add the left side using the LCD. 11d = 1980 Multiply each side by 300 and simplify. d = 180 Divide each side by 11 and simplify. The distance one way is 180 miles.

20. Step 3 Use the expressions from Step 1 to find the two trip times
Step 3 Use the expressions from Step 1 to find the two trip times. So, the delivery takes 180 mi ÷ 60 𝑚𝑖 1 ℎ = 3 hours, and the return trip takes 180 mi ÷ 50 𝑚𝑖 1 ℎ = 3.6 hours.

21. You Try! NO $
Delivery: 3h
Return: 4h

22. Workbook p. 25 & 26 (odd questions only)
Work with 1 partner. Each person must do their own work.