Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write an equation of each line.

10. slope = 3; through (1, 5)
11. slope = 5 6 ; 5 sixths , semicolon  through (22, 12)
12. slope = − 3 5 ; negative , 3 fifths , semicolon  through ( − 4 , 0 ) open negative 4 comma 0 close
13. slope = 0; through ( 4 , − 2 ) open 4 comma negative 2 close
14. slope = − 1 ; negative 1 semicolon  through ( − 3 , 5 ) open negative 3 comma 5 close
15. slope = 5; through (0, 2)

See Problem 2.

Write in point-slope form an equation of the line through each pair of points.

16. ( − 10 , 3 ) open negative 10 comma 3 close  and ( − 2 , − 5 ) open negative 2 comma negative 5 close
17. (1, 0) and (5, 5)
18. ( − 4 , 10 ) open negative 4 comma 10 close  and ( − 6 , 15 ) open negative 6 comma 15 close
19. ( 0 , − 1 ) open 0 comma negative 1 close  and ( 3 , − 5 ) open 3 comma negative 5 close
20. (7, 11) and (13, 17)
21. (1, 9) and (6, 2)

See Problem 3.

Write an equation of each line in standard form with integer coefficients.

22. y = 1 2 x − 2 y equals , 1 half , x minus 2
23. y = − 7 x − 9 y equals negative 7 x minus 9
24. y = − 3 5 x + 3 y equals negative , 3 fifths , x plus 3
25. y = 4.2 x + 7.9 y equals 4.2 x plus 7.9

See Problem 4.

Find the intercepts and graph each line.

26. x − 4 y = − 4 x minus , 4 y equals negative 4
27. 2 x + 5 y = − 10 2 x plus 5 y equals negative 10
28. − 3 x + 2 y = 6 negative 3 x plus 2 y equals 6
29. 5 x + 7 y = 14 5 x plus 7 y equals 14

See Problem 5.

Write and graph an equation to represent each situation.

30. You put 15 gallons of gasoline in your car. You know that this amount of gasoline will allow you to drive about 450 miles.
31. A meal plan lets students buy $20 meal cards. Each meal card lasts about 8 days.

See Problem 6.

Write the equation of the line through each point. Use slope-intercept form.

32. ( 1 , − 1 ) ; open 1 comma negative 1 close semicolon  parallel to y = 2 5 x − 3 y equals , 2 fifths , x minus 3
33. ( − 2 , 1 ) ; open negative 2 comma 1 close semicolon  perpendicular to y = − 2 5 x − 4 y equals negative , 2 fifths , x minus 4
34. ( − 2 , 10 ) ; open negative 2 comma 10 close semicolon  parallel to 2 x − 3 y = − 3 2 x minus 3 y equals negative 3
35. ( − 2 , 1 ) ; open negative 2 comma 1 close semicolon  perpendicular to 3 x + y = 1 3 x plus y equals 1

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