Preview Warm Up California Standards Lesson Presentation

Warm Up Write an equation for each relationship. Tell what each variable you use represents. 1. The length of a wall is 4 ft more than three times the height. 2. The number of trading cards is 3 less than the number of buttons. l = 3h + 4, where l is length and h is height. c = b – 3, where c is the number of cards and b is the number of buttons.

California Standards AF1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. Also covered: NS2.3

Vocabulary linear equation

You can also graph the solutions of an equation on a coordinate plane You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs given by some equations, they form a straight line. For this reason, these equations are called linear equations.

Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

Make a table by using the given values for x to find values for y. Additional Example 1: Finding Solutions of Equations with Two Variables Use the given x-values to write solutions of the equation as ordered pairs. y = 4x + 2; x = 1, 2, 3, 4. Make a table by using the given values for x to find values for y. Write these solutions as ordered pairs. x 4x + 2 y 1 4(1) + 2 6 2 4(2) + 2 10 3 4(3) + 2 14 4 4(4) + 2 18 (x, y) (1, 6) (2, 10) (3, 14) (4, 18)

Additional Example 2A: Checking Solutions of Equations with Two Variables Determine whether the ordered pair is a solution to the given equation. (3, 21); y = 7x Write the equation. y = 7x 21 = 7(3) ? Substitute 3 for x and 21 for y. 21 = 21 ?  So (3, 21) is a solution to y = 7x.

Additional Example 3: Reading Solutions on Graphs Use the graph of the linear equation to find the value of y for the given value of x. x = 4 Start at the origin and move 4 units right. x y -4 -2 0 2 4 4 -2 -4 2 Move up until you reach the graph. Move left to find the y-value on the y-axis. When x = 4, y = 2. The ordered pair is (4, 2).

Additional Example 4: Graphing Linear Functions Graph the equation y = –x – 2. Make a table. Substitute different values for x. Write the solutions as ordered pairs. x –x – 2 y –1 –(–1) – 2 –(0) – 2 –2 1 –(1) – 2 –3 (x, y) (–1, –1) (0, –2) (1, –3)

Additional Example 4 Continued Graph the ordered pairs on a coordinate plane. x y 5 4 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5

Write these solutions as ordered pairs. Check It Out! Example 1 Use the given x-values to write solutions of the equation as ordered pairs. y = 3x + 2; x = 2, 3, 4, 5. Make a function table by using the given values for x to find values for y. Write these solutions as ordered pairs. x 3x + 2 y 2 3(2) + 2 8 3 3(3) + 2 11 4 3(4) + 2 14 5 3(5) + 2 17 (x, y) (2, 8) (3, 11) (4, 14) (5, 17)

Check It Out! Example 2A Determine whether the ordered pair is a solution to the given equation. (4, 20); y = 5x Write the equation. y = 5x 20 = 5(4) ? Substitute 4 for x and 20 for y. 20 = 20 ?  So (4, 20) is a solution to y = 5x.

Start at the origin and move 2 units right. Check It Out! Example 3 Use the graph of the linear function to find the value of y for the given value of x. x = 2 Start at the origin and move 2 units right. x y -4 -2 0 2 4 4 -2 -4 2 Move up until you reach the graph. Move left to find the y-value on the y-axis. When x = 2, y = 4. The ordered pair is (2, 4).

Check It Out! Example 4 Graph the equation. y = –x – 4 Make a table. Substitute different values for x. Write the solutions as ordered pairs. x –x – 4 y –1 –(–1) – 4 –3 –(0) – 4 –4 1 –(1) – 4 –5 (x, y) (–1, –3) (0, –4) (1, –5)

Check It Out! Example 4 Continued Graph the ordered pairs on a coordinate plane. x y 5 4 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5

3. Graph the function described by the equation y = –x + 3. Lesson Quiz 1. Use the given x-values to write solutions as ordered pairs to the equation y = –3x + 1 for x = 0, 1, 2, and 3. 2. Determine whether (4, –2) is a solution to the equation y = –5x + 3. 3. Graph the function described by the equation y = –x + 3. (0, 1), (1, –2), (2, –5), (3, –8) No, –2 ≠ –5(4) + 3