1. Holt CA Course 1 2-8 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

2. Holt CA Course 1 2-8 Graphing Equations Vocabulary linear equation An equation whose solutions form a straight line on a coordinate plane.

3. Holt CA Course 1 2-8 Graphing Equations 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) + 26 24(2) + 210 34(3) + 214 44(4) + 218 Write these solutions as ordered pairs. (x, y) (1, 6) (2, 10) (3, 14) (4, 18)

4. Holt CA Course 1 2-8 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.

5. Holt CA Course 1 2-8 Graphing Equations Example 2: 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.

6. Holt CA Course 1 2-8 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. 

7. Holt CA Course 1 2-8 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. 

8. Holt CA Course 1 2-8 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.

9. Holt CA Course 1 2-8 Graphing Equations 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 -4 -2 0 2 4 4 -2 -4 2

10. Holt CA Course 1 2-8 Graphing Equations 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)

11. Holt CA Course 1 2-8 Graphing Equations Example 4 Continued x y Graph the ordered pairs on a coordinate plane. -5 -4 -3 -2 -1 0 1 2 3 4 5 5 4 3 2 1 -5 -4 -3 -2 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.

12. Holt CA Course 1 2-8 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) + 28 33(3) + 211 43(4) + 214 53(5) + 217 Write these solutions as ordered pairs. (x, y) (2, 8) (3, 11) (4, 14) (5, 17)

13. Holt CA Course 1 2-8 Graphing Equations Check It Out! Example 2 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, yes (4, 20) is a solution to y = 5x.

14. Holt CA Course 1 2-8 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 -4 -2 0 2 4 4 -2 -4 2

15. Holt CA Course 1 2-8 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)

16. Holt CA Course 1 2-8 Graphing Equations Check It Out! Example 4 Continued x y Graph the ordered pairs on a coordinate plane. -5 -4 -3 -2 -1 0 1 2 3 4 5 5 4 3 2 1 -5 -4 -3 -2 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.