Linear Functions TLW identify linear equations and intercepts

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

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

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

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

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.

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

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 + 20 y = 12 A = 1, B= 20, C=12 This IS a linear equation.

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

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 (0, y) X- intercept (-x, 0)

Graph the linear equation using the x - intercept and the y intercept 3 x + 2 y = 9 To find the x- intercept, let y = 0 Original Equation 3 x + 2 y = 9 3 x + 2(0) = 9 3 x = 9 x=3 Replace y with 0 Divide each side by 3 To find the y- intercept, let x = 0 Original Equation 3 x + 2 y = 9 3(0) + 2 y = 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 2 x + y = 4 To find the x- intercept, let y = 0 2 x + y = 4 Original Equation 2 x + (0) = 4 2 x =4 x=2 Replace y with 0 Divide each side by 3 To find the y- intercept, let x = 0 2 x + 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 -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 = 4 y – 5 ● ● ● x-intercept: Plug in y = 0 x = 4 y - 5 x = 4(0) - 5 x=0 -5 x = -5 (-5, 0) is the x-intercept ● ● ● y-intercept: Plug in x = 0 x = 4 y - 5 0 = 4 y - 5 5 = 4 y =y (0, ) is the y-intercept

Find the x and y-intercepts of g(x) = -3 x – 1* ● ● ● x-intercept Plug in y = 0 g(x) = -3 x - 1 0 = -3 x - 1 1 = -3 x =x ( , 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 6 x - 3 y =-18 ● ● ● x-intercept Plug in y = 0 6 x - 3 y = -18 6 x -3(0) = -18 6 x - 0 = -18 6 x = -18 x = -3 (-3, 0) is the x-intercept ● ● ● y-intercept Plug in x = 0 6 x -3 y = -18 6(0) -3 y = -18 0 - 3 y = -18 -3 y = -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 Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points x y (x, y) -2 0 -4 -3 (-2, -4) (0, -3) 2 -2 (2, -2)

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 x y (x, y)

Questions? ?