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Linear Functions

Linear Functions. TLW identify linear equations and intercepts. A linear equation is the equation of a line. The standard form of a linear equation is Ax + By = C * A has to be positive and cannot be a fraction. Examples of linear equations. Equation is in A x + B y =C form

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Linear Functions

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  1. Linear Functions TLW identify linear equations and intercepts.

  2. A linear equation is the equation of a line. The standard form of a linear equation is Ax + By = C * A has to be positive and cannot be a fraction.

  3. Examples of linear equations Equation is in Ax + By =C form Rewrite with both variables on left side … x + 6y =3 B=0 … x + 0 y =1 Multiply both sides of the equation by -1 … 2a – b = -5 Multiply both sides of the equation by 3 … 4x –y =-21 2x + 4y =8 6y = 3 – x x = 1 -2a + b = 5

  4. Examples of Nonlinear Equations The following equations are NOT in the standard form of Ax + By =C: 4x2 + y = 5 xy + x = 5 s/r + r = 3 The exponent is 2 There is a radical in the equation Variables are multiplied Variables are divided

  5. Determine whether the equation is a linear equation, if so write it in standard form. y = 5 – 2x Rewrite the equation y = 5 – 2x + 2x + 2x Add 2x to each side 2x + y = 5 Simplify A = 2, B= 1, C=5 This IS a linear equation.

  6. Determine whether the equation is a linear equation, if so write it in standard form. 2xy -5y = 6 Since the term 2xy has two variables, the equation cannot be written in the form Ax + By =0. Therefore, this is NOT a linear equation.

  7. Determine whether the equation is a linear equation, if so write it in standard form. Since the term x is raised to the second power, the equation cannot be written in the form Ax + By =0. Therefore, this is NOT a linear equation.

  8. Determine whether the equation is a linear equation, if so write it in standard form. y = 6 – 3x Rewrite the equation y = 6 – 3x Add 3x to each side + 3x + 3x 3x +y = 6 Simplify A = 3, B= 1, C=6 This IS a linear equation.

  9. Determine whether the equation is a linear equation, if so write it in standard form. Multiply everything by the denominator to get rid of the fraction (4) x + 20y = 12 A = 1, B= 20, C=12 This IS a linear equation.

  10. Determine whether the equation is a linear equation, if so write it in standard form. -4x+7=2

  11. X and Y intercepts The x coordinate of the point at which the graph of an equation crosses the x –axis is the x- intercept . The y coordinate of the point at which the graph of an equation crosses the y-axis is called the y- intercept. y- intercept (0, y) X- intercept (-x,0)

  12. Graph the linear equation using the x- intercept and the y intercept 3x + 2y = 9 To find the x- intercept, let y = 0 Original Equation 3x + 2y = 9 3x + 2(0) = 9 Replace y with 0 3x = 9 Divide each side by 3 x = 3 To find the y- intercept, let x = 0 Original Equation 3x + 2y = 9 3(0) + 2y = 9 Replace x with 0 2y = 9 Divide each side by 2 y = 4.5 Plot the two points and connect them to draw the line.

  13. Graph the linear equation using the x- intercept and the y intercept 2x + y = 4 To find the x- intercept, let y = 0 2x + y = 4 Original Equation 2x + (0) = 4 Replace y with 0 Divide each side by 3 2x =4 x = 2 To find the y- intercept, let x = 0 2x + y = 4 Original Equation 2(0) + y = 4 Replace x with 0 Simplify y = 4 Plot the two points and connect them to draw the line.

  14. Identify the x- and y- intercepts given a table

  15. x-intercept: Plug in y = 0 x = 4y - 5 x = 4(0) - 5 x = 0 - 5 x = -5 (-5, 0) is the x-intercept y-intercept: Plug in x = 0 x = 4y - 5 0 = 4y - 5 5 = 4y = y (0, ) is the y-intercept Find the x and y- interceptsof x = 4y – 5

  16. x-intercept Plug in y = 0 g(x) = -3x - 1 0 = -3x - 1 1 = -3x = x ( , 0) is the x-intercept y-intercept Plug in x = 0 g(x) = -3(0) - 1 g(x)= 0 - 1 g(x) = -1 (0, -1) is the y-intercept Find the x and y-interceptsof g(x) = -3x – 1* *g(x) is the same as y

  17. x-intercept Plug in y = 0 6x - 3y = -18 6x -3(0) = -18 6x - 0 = -18 6x = -18 x = -3 (-3, 0) is the x-intercept y-intercept Plug in x = 0 6x -3y = -18 6(0) -3y = -18 0 - 3y = -18 -3y = -18 y = 6 (0, 6) is the y-intercept Find the x and y-intercepts of 6x - 3y =-18

  18. x y Find the x and y-intercepts of x = 3 • y-intercept • A vertical line never crosses the y-axis. • There is no y-intercept. • x-intercept • Plug in y = 0. There is no y. Why? • x = 3 is a verticalline so x always equals 3. • (3, 0) is the x-intercept.

  19. x y Find the x and y-intercepts of y = -2 • x-intercept • Plug in y = 0. y cannot = 0 because y = -2. • y = -2 is a horizontal line so it never crosses the x-axis. • There is no x-intercept. • y-intercept • y = -2 is a horizontal line so y always equals -2. • (0,-2) is the y-intercept.

  20. Graph by making a table Graph Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points -4 (-2, -4) -2 0 -3 (0, -3) -2 (2, -2) 2

  21. Graph by making a table Graph Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points

  22. Questions??

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