Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find the x - and y-intercepts of the graph of each equation.

8. x + y = 9 x plus y equals 9
9. x − 2 y = 2 x minus 2 y equals 2
10. − 3 x + 3 y = 7 negative 3 x plus 3 y equals 7
11. 3 x − 5 y = − 20 3 x minus 5 y equals negative 20
12. 7 x − y = 21 7 x minus y equals 21
13. − 5 x + 3 y = − 7.5 negative 5 x plus 3 y equals negative 7.5

See Problem 2.

Draw a line with the given intercepts.

14. x-intercept: 3

    y-intercept: 5

15. x-intercept: − 1 negative 1

    y-intercept: − 4 negative 4

16. x-intercept: 4

    y-intercept: − 3 negative 3

Graph each equation using x - and y-intercepts.

17. x + y = 4 x plus y equals 4
18. x + y = − 3 x plus y equals negative 3
19. x − y = − 8 x minus y equals negative 8
20. − 2 x + y = 8 negative 2 x plus y equals 8
21. − 4 x + y = − 12 negative 4 x plus y equals negative 12
22. 6 x − 2 y = 18 6 x minus 2 y equals 18

See Problem 3.

For each equation, tell whether its graph is a horizontal or a vertical line.

23. y = − 4 y equals negative 4
24. x = 3 x equals 3
25. y = 7 4 y equals , 7 fourths
26. x = − 1.8 x equals negative 1.8

Graph each equation.

27. y = 6 y equals 6
28. x = − 3 x equals negative 3
29. y = − 2 y equals negative 2
30. x = 7 x equals 7

See Problem 4.

Write each equation in standard form using integers.

31. y = 2 x + 5 y equals 2 x plus 5
32. y + 3 = 4 ( x − 1 ) y plus 3 equals 4 open x minus 1 close
33. y − 4 = − 2 ( x − 3 ) y minus 4 equals negative 2 open x minus 3 close
34. y = 1 4 x − 2 y equals , 1 fourth , x minus 2
35. y = − 2 3 x − 1 y equals negative , 2 thirds , x minus 1
36. y + 2 = 2 3 ( x + 4 ) y plus 2 equals , 2 thirds , open x plus 4 close

    See Problem 5.

37. Video Games In a video game, you earn 5 points for each jewel you find. You earn 2 points for each star you find. Write and graph an equation that represents the numbers of jewels and stars you must find to earn 250 points. What are three combinations of jewels and stars you can find that will earn you 250 points?
38. Clothing A store sells T-shirts for $12 each and sweatshirts for $15 each. You plan to spend $120 on T-shirts and sweatshirts. Write and graph an equation that represents this situation. What are three combinations of T-shirts and sweatshirts you can buy for $120?

B Apply

39. Writing The three forms of linear equations you have studied are slope-intercept form, point-slope form, and standard form. Explain when each form is most useful.

40. Think About a Plan You are preparing a fruit salad. You want the total carbohydrates from pineapple and watermelon to equal 24 g. Pineapple has 3 g of carbohydrates per ounce and watermelon has 2 g of carbohydrates per ounce. What is a graph that shows all possible combinations of ounces of pineapple and ounces of watermelon?

    • Can you write an equation to model the situation?
    • What domain and range are reasonable for the graph?

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