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Write an equation in y=mx+b 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 2x + 4y =8 6y = 3 – x Equation is in Ax + By =C form Rewrite with both variables on left side … x + 6y =3 B =0 … x + 0 y =1 x=1 -2a + b = 5 4x y 7 3 Multiply both sides of the equation by -1 … 2a – b = -5 Multiply both sides of the equation by 3 … 4x –y =-21 Examples of Nonlinear Equations The following equations are NOT in the standard form of Ax + By =C: 4x2 + y = 5 x4 xy + x = 5 s/r + r = 3 The exponent is 2 There is a radical in the equation Variables are multiplied Variables are divided 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) 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 3x = 9 x=3 Replace y with 0 Divide each side by 3 To find the y- intercept, let x = 0 Original Equation 3x + 2y = 9 3(0) + 2y = 9 2y = 9 y = 4.5 Replace x with 0 Divide each side by 2 Plot the two points and connect them to draw the line. 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 2x =4 x=2 Replace y with 0 Divide each side by 3 To find the y- intercept, let x = 0 2x + y = 4 Original Equation 2(0) + y = 4 y=4 Replace x with 0 Simplify Plot the two points and connect them to draw the line. Identify the x- and y- intercepts given a table X Y X Y -1 -6 -4 1 0 -4 -3 0 1 -2 -2 -1 2 0 -1 -2 3 2 0 -3 Find the x and y- intercepts of x = 4y – 5 ● ● ● 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 5 =y 4 5 ● (0, ) 4 is the y-intercept Find the x and y-intercepts of g(x) = -3x – 1* ● ● ● x-intercept Plug in y = 0 g(x) = -3x - 1 0 = -3x - 1 1 = -3x 1 =x 3 1 ( 3 , 0) is the x-intercept *g(x) is the same as y ● ● ● 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-intercepts of 6x - 3y =-18 ● ● ● 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 x = 3 ● ● x-intercept Plug in y = 0. There is no y. Why? ● y-intercept ●A vertical line never crosses the y-axis. ● There is no y-intercept. x = 3 is a vertical line so x always equals 3. ● ● x (3, 0) is the x-intercept. 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 ● y-intercept ● y = -2 is a horizontal line so y always equals -2. ● (0,-2) is the y-intercept. x is no x-intercept. y Graph by making a table Graph y 1 x 3 2 Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points x -2 0 2 1 x3 2 1 ( 2) 3 2 1 (0) 3 2 1 ( 2) 3 2 y (x, y) -4 -3 (-2, -4) (0, -3) -2 (2, -2) Describe the error in finding the X intercept and find the correct x intercept Questions??