Over Lesson 8–2 A.A B.B C.C D.D 5-Minute Check 1 Which equation best describes the sequence 9, 10, 11, 12, …? Find the 22nd term of the sequence 7, 10, 13, 16, …. Jimmy increased his trumpet practice by 10 minutes each week. He practiced 15 minutes during Week 1. How many minutes did he practice during Week 12?

Splash Screen

Then/Now You used functions to describe relationships between two quantities. (Lesson 1–5) Solve linear equations with two variables. Graph linear equations using ordered pairs.

Vocabulary linear equation x-intercept y-intercept An equation in which the variables appear in separate terms and neither variable contains an exponent other than 1. The graph of a linear equation is a straight line. The x-coordinate of a point where a graph crosses the x-axis (x, 0) The y-coordinate of a point where a graph crosses the y-axis (0, y)

Example 1 Use a Table of Ordered Pairs Find four solutions of y = 4x + 3. Write the solutions as ordered pairs. Choose four values for x. Then substitute each value into the equation to solve for y. There are many possible solutions. The solutions you find depend on which x-values you choose.

Example 1 Use a Table of Ordered Pairs Sample Answer: Four possible solutions are (0, 3), (1, 7), (2, 11), and (3, 15).

A.A B.B C.C D.D Example 1 A.(1, –2), (3, 2), (5, 1), and (7, 10) B.(–2, 0), (0, –4), (2, 0), and (4, 4) C.(0, –4), (1, –2), (2, 2), and (3, –1) D.(0, –4), (1, –2), (2, 0), and (3, 2) Find four solutions of y = 2x – 4.

Example 2 Use Function Equations BUSINESS At a local software company, Level 1 employees x earn $48,000 and Level 2 employees y earn $24,000. Find four solutions of 48,000x + 24,000y = 216,000 to determine how many employees at each level the company can hire for $216,000. Explain each solution. First, rewrite the equation by solving for y.

Example 2 Use Function Equations 48,000x + 24,000y=216,000Write the equation. 24,000y=216,000 – 48,000xSubtract 48,000x from each side. Divide each side by 24,000. y=9 – 2xSimplify.

Example 2 Use Function Equations Choose four x-values and substitute them into y = 9 – 2x. Sample Answer:(0, 9), (1, 7), (2, 5), and (3, 3) 0 employees at Level 1, 9 employees at Level 2 1 employee at Level 1, 7 employees at Level 2 2 employees at Level 1, 5 employees at Level 2 3 employees at Level 1, 3 employees at Level 2

A.A B.B C.C D.D Example 2 A.0 hardbacks, 42 paperbacks 3 hardbacks, 24 paperbacks 5 hardbacks, 12 paperbacks 7 hardbacks, 0 paperbacks B.0 hardbacks, 14 paperbacks 1 hardbacks, 12 paperbacks 2 hardbacks, 10 paperbacks 3 hardbacks, 8 paperbacks C.0 hardbacks, 42 paperbacks 3 hardbacks, 24 paperbacks 5 hardbacks, 9 paperbacks 7 hardbacks, 7 paperbacks D.0 hardbacks, 14 paperbacks 1 hardbacks, 8 paperbacks 2 hardbacks, 2 paperbacks 3 hardbacks, –4 paperbacks BOOKS At a local bookstore, hardbacks are on sale for $6 and paperbacks are on sale for $3. Bob has $42 to spend on books. Find four solutions to determine how many books of each type Bob can buy with his $42.

Example 3 Graph a Linear Function Graph y = x + 2. Step 1Find the x-intercept. To find the x-intercept, let y = 0. y=x + 2Write the equation. 0=x + 2Replace y with 0. –2=xSubtract 2 from each side. Since x = –2 when y = 0, graph the ordered pair (–2, 0).

Example 3 Graph a Linear Function Step 2Find the y-intercept. y=x + 2Write the equation. y=0 + 2Replace x with 0. y=2Simplify. Since y = 2 when x = 0, graph the ordered pair (0, 2). Step 3Connect the points with a line.

Example 3 Graph a Linear Function CheckCheck another point in the equation. If x = 1, y = or 3. Notice that (1, 3) is on the graph of the line.

A.A B.B C.C D.D Example 3 Graph y = 5 – x. A.B. C.D.

End of the Lesson