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Chapter 2.2

Chapter 2.2. Linear Equations. WARM UP!. 1 3 5 7. Find w(-2) if w(x) = 3w + 8. 3 2 -1. Is this a function?. By the end of this lesson you will be able to:. Know what a linear equation is Know what a linear function is Put a linear equation in standard form

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Chapter 2.2

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  1. Chapter 2.2 Linear Equations

  2. WARM UP! 1 3 5 7 Find w(-2) if w(x) = 3w + 8 3 2 -1 Is this a function?

  3. By the end of this lesson you will be able to: • Know what a linear equation is • Know what a linear function is • Put a linear equation in standard form • Graph a line using the x and y intercepts

  4. Linear Equations: • An equation such as x + y = 4 is called a linear equation • They have no operations other than addition, subtraction, and multiplication of a variable by a constant.

  5. Linear Equations Continued: • The variables may not be multiplied together or appear in a denominator. • A linear equation does not contain variables with exponents other than one.

  6. Examples: Linear Equations: Not Linear Equations: 5x – 3y = 7 7a + 4b2 = -8 Y = ¾x x + xy = 1 X = 9 y =

  7. Linear Functions: • A Linear Function that can be written as Y=mx +b where m and b are real numbers • For example: • F(x) = 10 – 5x (yes) • F(x) = x4 -5 (no) • F(x) = 2xy (no)

  8. Standard Form: • The standard form of a linear equation is Ax + By = C • A and B must be whole numbers • A must be positive • So… manipulate the equation so that both x and y are on the same side of the equal sign and that the coefficients are not decimals or fractions.

  9. Finding X and Y Intercepts: 3x + 2y = 8 • To find the X-intercept – set the y variable equal to zero • To find the Y-intercept – set the x variable equal to zero

  10. Graphing Using the X and Y Intercepts: • Once you find both intercepts, plot them on the same coordinate plane. • Connect the points with a line. • This is the graph of the equation.

  11. Tonight’s Homework: Page 66 (15-23 odd) (27-49 odd)

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