1 / 28

y = mx + b

Introduction to Solving Equations. y = mx + b. ax + by = c. Lesson 1.6. Objectives. Write and solve a linear equation in one variable. Solve a literal equation for a specified variable. Glossary Terms. Equation like terms literal equation solution Substitution Property terms

vilina
Download Presentation

y = mx + b

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Solving Equations y = mx + b ax + by = c Lesson 1.6

  2. Objectives • Write and solve a linear equation in one variable. • Solve a literal equation for a specified variable. Glossary Terms Equationlike terms literal equation solution Substitution Property terms variable

  3. a b = c c Division If a = b, then , where c  0. Rules and Properties Reflexivea = a Symmetric If a = b, then b = a. Transitive If a = b and b = c, then a = c. Addition If a = b, then a + c = b + c. Subtraction If a = b, then a – c = b – c. Multiplication If a = b, then ac = bc.

  4. Solving Linear Equations To solve a simple equation use the inverse operation Add 3 to both sides of the equation X - 3 = -15 X= -12 Subtract 5 from both sides of the equation X + 5 = -4 X = -9

  5. Solving Linear Equations To solve a simple equation use the inverse operation Divide both sides of the equation by -3 -3X = 45 X = -15 X/-4 = 5 Multiply both sides of the equations by -4 X = -20

  6. Solving Linear Equations To solve a simple equation use the inverse operation Multiply both sides of the equation by the reciprocal of the fraction. (-2/3)X = 4 X = -6

  7. Solving Linear Equations Two step equationsAdd/Subtract first Multiply/Divide second Subtract 6, divide by -4 -4X + 6 =-14 X = 5 Add 5, multiply by 3 X/3 - 5 = -2 X = 9

  8. Solving Linear Equations Multi-step equations Simplify both sides of the equation by combining like terms -4X -13 + 5x = 36 - 17 Combine -4x + 5x and 36 - 17 Add 13 to both sides of the equation X - 13 = 19 X = 32

  9. Solving Linear Equations Variables on both sides of the equation Eliminate the variable on one side of the equation by doing the inverse operation. Subtract 2x from both sides of the equation -3X + 5 = 2x - 10 -5X + 5 = -10 Subtract 5, divide by -5 X = 3

  10. Solving Linear Equations Using the Distributive Property When parentheses are present, the first step is to remove them using the distributive property. -2(X - 4) = -20 Remove parentheses -2x + 8 = -20 Subtract 8, divide by -2 X = 14

  11. Solving Linear Equations - A Summary 1. Remove Parentheses 2. Combine like terms. Eliminate all but one term with a variable. 3. Add/Subtract 4. Multiply/Divide

  12. Solving Linear Equations PRACTICE TIME!

  13. 1. 3(2z + 1) = 35 2. t - 2(3 - 2t) = 2t + 9 3. 5(3w - 2) - 7 = 23 4. 8(s - 12) - 24 = 3(s + 2)

  14. Solving Equations Graphically In the equation x + 3 = 9 - 2x, what two expressions are equal? Use a graphing calculator to graph y = x + 3 and 9 - 2x on the same screen. For what value of x do they have the same value?

  15. Graphic Solutions The x-coordinate of the point where the graphs intersect is the solution. X = 2

  16. Solving Literal Equations 2a - 3b + x = 9 I = Prt F = (9/5)C + 32

  17. Literal Equations A literal equation is an equation that contains two or more variables. Formulas are examples of literal equations.

  18. To solve literal equations, use the same properties of equality for solving any equation. Follow the same steps to isolate or “solve for” the indicated variable. The equation I = Prt relates the simple interest (I), principal (P), interest rate (r), and time (t) for an investment.

  19. Solve I = Prt for r I = Prt Pt Pt So r = I Pt Solve I = Prt for P I rt P =

  20. Restrictions in literal equations Solve ax = t for x ax = t Therefore x = t/aa a Since there is a variable in the denominator, you must exclude any values of the variable that make the denominator = 0. Thus a  0.

  21. Solve for x and indicate any restrictions on the values of the variables. a. ax + b = c x = (c - b)/a, a  0 b. x/r - h = 4, r  0 x = r(4 + h)

  22. c. d - x = e x = -e + d d. y - px - c = bk x = (-bk + y - c)/p, p  0 e. Solve C = (5/9)(F - 32) for F F = (9/5)C + 32

  23. f. Solve cx + dx = e for x (Hint: factor out x) x = e/(c + d), c  -d g. Solve kt = (t/2) + r for t t = 2r/(2k - 1), k  1/2 h. Solve 1/x + a = b, for x x  0 x = 1/(b - a), b  0

  24. Young’s formula is used to relate a child’s dose of a medication to an adult’s dose of the same medication. The formula applies to children from 1 to 12 years old.

  25. Equations with no solution Solve: 5(3 - x) = 2 - 5x 15 - 5x = 2 - 5x (Dist. Prop) 15 = 2 (Addition prop) Because this is a false statement, there is no solution to this equation. There are no values of x that make this equation a true equation.

  26. Homework p. 49 (35 - 38, 41 - 42, 47 - 56)

  27. The End

More Related