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Mastering Linear Equations: Definitions and Graphing Techniques

Learn definitions of linear equations and functions, put equations in standard form, and graph lines using intercepts. Explore examples and understand concepts thoroughly. Complete homework on page 66.

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Mastering Linear Equations: Definitions and Graphing Techniques

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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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