1. Preview
Warm Up
California Standards
Lesson Presentation

2. 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.

3. 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

4. Vocabulary
linear equation

5. 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.

6. 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.

7. 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)

8. 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.

9. 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 -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).

10. 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)

11. 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 -1 -2 -3 -4 -5

12. 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)

13. 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.

14. 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 -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).

15. 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)

16. 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 -1 -2 -3 -4 -5

17. 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