3-3A Linear Functions Algebra 1 Glencoe McGraw-HillLinda Stamper

In Chapter 2 you solved linear equations. In a linear equation the exponent of the variable is one. 1 In this lesson you will graph linear equations in two variables. In a linear equation with two variables the exponent of the variables is one. 1 1

A linear equation in x and y is an equation that can be written in the form Ax + By = C. This is the standard form of a linear equation! The A is the coefficient of the x term while the B is the coefficient of the y term! C represents a constant.

Explain why the following equations are NOT considered to be in standard form. In standard form A > 0, and A and B are not both zero and A, B, and C are integers with a greatest common factor of 1. x and y need to be on the left side of equal sign. x term comes before the y term. “A” needs to be greater than or equal to one. “A” is not an integer. GCF of A, B, and C is not 1.

Determine whether y = 5 – 2x is a linear equation. If so, write the equation in standard form. Determine if linear equation. Write in standard form. Add 2x to each side. Simplify. Since the x and y terms are to the first degree, it is a linear equation.

Determine whether each equation is a linear equation. If so, write the equation in standard form. Example 1 5x + 3y = z + 2 Since there are 3 variables it is not a linear equation. Example 2 no Example 3 Since the term 2xy has two variables, the equation is not a linear equation. no

Graphing Linear Equations All graphs must be completed neatly on graph paper. Show your support work next to the graph on the graph paper or it can be completed on regular notebook paper.

The graph of an equation in x and y is the set of all points (x,y) that are solutions of the equation. x y A default increment of one will be used if no increment values are on the graph. Label your graph if you are using an increment other than one. Draw and label the x and y axis on your graph. The graph of a linear equation is a straight line. The root word for linear is line.

Graphing A Linear Equation Solve the equation for y, if necessary. Choose at least three values of x and make a table of values. Choose values that will produce integer coordinates. Plot the points from the table of values and draw a line through the points. All points on the line are solutions of the equation. x y Draw the line through the entire graph. Use arrowheads!

Graph the equation –2x + y = –3. Write equation. Solve the equation for y. Choose any three values for x, and make a table of values. It is a good idea to use positive and negative values. Choose values that will produce integer coordinates. Reminder: place the variable term before the constant. The x is the independent variable and the y is the dependent variable. The best values to choose when the coefficient of x is an integer is -1, 0, 1

Graph –2x + y = –3. Create a table of values. Plot the points and draw a line through them. x y x y = 2x – 3(x,y) The x is the independent variable and the y is the dependent variable.

Graph the equation –x + 4y = –4. Write equation. Solve the equation for y. Choose any three values for x, and make a table of values. It is a good idea to use positive and negative values. Choose values that will produce integer coordinates. Reminder: place the variable term before the constant. The best values to choose for fractional coefficient of x are multiples of the denominator and zero.

Efficient values to choose for x. It is a good idea to use positive and negative values. Choose values that will produce integer coordinates. When the equation is solved for y and the coefficient of the x term is a fraction, choose multiples of the denominator. When the equation is solved for y and the coefficient of the x term is an integer, choose -1, 0, and 1.

Graph –x + 4y = –4. Create a table of values. Plot the points and draw a line through them. x y x (x,y)

Example 4 Graph the equation -½x + y = –3. Example 5 Graph the equation x – 3y = –9. Example 6 Graph 2x – 4y = –16. Write equation. Solve the equation for y. Choose any three values for x, and make a table of values. Choose values that will produce integer coordinates. Plot the points from the table of values and draw a line through the points. All points on the line are solutions of the equation.

Example 4 Graph the equation -½x + y = –3. Since you can choose any values for x, use values which are multiples of 2 to avoid graphing fractional values.

x(x,y) x y Example 4 Graph the equation -½x + y = –3.

Example 5 Graph the equation x – 3y = –9. Since you can choose any values for x, use values which are multiples of 3 to avoid graphing fractional values.

x(x,y) x y Example 5 Graph the equation x – 3y = –9.

Example 6 Graph 2x – 4y = –16. Since you can choose any values for x, use values which are multiples of 2 to avoid graphing fractional values.

x(x,y) x y Example 6 Graph 2x – 4y = –16.

3-A4 Pages 159–161 #12–17,25,28–30,64–70.