Holt CA Course Graphing Equations Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

Holt CA Course Graphing Equations 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.

Holt CA Course Graphing Equations 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 California Standards

Holt CA Course Graphing Equations Vocabulary linear equation

Holt CA Course Graphing Equations 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. x4x + 2y 14(1) (2) (3) (4) Write these solutions as ordered pairs. (x, y) (1, 6) (2, 10) (3, 14) (4, 18)

Holt CA Course Graphing Equations 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. x3x + 2y 23(2) (3) (4) (5) Write these solutions as ordered pairs. (x, y) (2, 8) (3, 11) (4, 14) (5, 17)

Holt CA Course Graphing 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.

Holt CA Course Graphing Equations 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 y = 7x Write the equation. 21 = 7(3) ? 21 = 21 ? Substitute 3 for x and 21 for y. So (3, 21) is a solution to y = 7x.

Holt CA Course Graphing Equations Additional Example 2B: Checking Solutions of Equations with Two Variables Determine whether the ordered pair is a solution to the given equation. (–3, –4); y = x + 7 y = x + 7 Write the equation. –4 = –3 + 7 ? –4 ≠ 4 Substitute –3 for x and –4 for y. So (–3, –4) is not a solution to y = x + 7. 

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

Holt CA Course Graphing Equations Check It Out! Example 2B Determine whether the ordered pair is a solution to the given equation. (–3, –2); y = x + 5 y = x + 5 Write the equation. –2 = –3 + 5 ? –2 ≠ 2 Substitute –3 for x and –2 for y. So (–3, –2) is not a solution to y = x + 5. 

Holt CA Course Graphing Equations 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.

Holt CA Course Graphing Equations 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 When x = 4, y = 2. Start at the origin and move 4 units right. Move up until you reach the graph. Move left to find the y-value on the y-axis. The ordered pair is (4, 2). x y

Holt CA Course Graphing Equations 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 When x = 2, y = 4. Start at the origin and move 2 units right. Move up until you reach the graph. Move left to find the y-value on the y-axis. The ordered pair is (2, 4). x y

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

Holt CA Course Graphing Equations Additional Example 4 Continued x y Graph the ordered pairs on a coordinate plane Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.

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

Holt CA Course Graphing Equations Check It Out! Example 4 Continued x y Graph the ordered pairs on a coordinate plane Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.

Holt CA Course Graphing Equations 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 Determine whether (4, –2) is a solution to the equation y = –5x Graph the function described by the equation y = –x + 3. No, –2 ≠ –5(4) + 3 (0, 1), (1, –2), (2, –5), (3, –8)