Exercises
Name _______________________________ (2-4)A
GUIDED PRACTICE
Graph the line with the given slope that contains the given point.
1
1. slope = 1; (1, 0)
p. 341
XAMPLE
3. slope = -2; (-4, -2)
Write an equation in point-slope form for the line with the given slope that contains the given point. 1 ; 2, -6 4. slope = _ 5. slope = -4; (1, 5) 6. slope = 0; (3, -7) ) ( 5
3
Write an equation in slope-intercept form for the line with the given slope that contains the given point. 1 ; -3, 8 1 ; -6, -2 7. slope = - _ 8. slope = 2; (1, 1) 9. slope = _ ) ) ( ( 3 3
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10. slope = 2; (-1, 1)
XAMPLE 4 p. 343
XAMPLE
2. slope = -1; (3, 1)
2
p. 342
XAMPLE
S s ’ e T s H s WRIG Cl a KEYWORD: MA7 Parent
(2-4)A Writing Linear Equations
XAMPLE
5
p. 343
11. slope = 3; (2, -7)
12. slope = -4; (4, 2)
Write an equation in slope-intercept form for the line through the two points. 13.
(-2, 2) and (2, -2)
14.
(0, -4) and (1, -6)
15.
(1, 1) and (-5, 3)
16.
(-3, 1) and (0, 10)
17.
(7, 8) and (6, 9)
18.
(0, -2) and (2, 8)
19. Measurement An oil tank is being filled at a constant rate. The depth of the oil is a function of the number of minutes the tank has been filling, as shown in the table. Write an equation in slope-intercept form that represents this linear function. Then find the depth of the oil after one-half hour.
Time (min)
Depth (ft)
0
3
10
5
15
6
PRACTICE AND PROBLEM SOLVING
dent Practice See es Example
2 8 4 0
KEYWORD: MA7 5-7
1 2 3 4 5
Practice
ice p. S13
n Practice p. S32
Graph the line with the given slope that contains the given point. 3 ; 1, -2 1 ; -3, 4 20. slope = - _ 21. slope = _ 22. slope = 4; (-1, 0) ) ) ( ( 5 2 Write an equation in point-slope form for the line with the given slope that contains the given point. 2 ; -1, 5 23. slope = _ 24. slope = 0; (4, -2) 25. slope = 8; (1, 8) ) ( 9 1 ; -8, 3 27. slope = 3; (4, 7) 28. slope = -2; (-1, 3) 26. slope = _ ) ( 2 Write an equation in slope-intercept form for the line with the given slope that contains the given point. 2 ; 14, -3 1 ; 4, -1 4 ; -15, 1 29. slope = - _ 30. slope = _ 31. slope = - _ ) ) ) ( ( ( 7 4 5 1 ; -5, -2 33. slope = -5; (2, 3) 34. slope = _ 32. slope = -6; (9, 3) ) ( 5 Write an equation in slope-intercept form for the line through the two points. 35.
(7, 8) and (-7, 6)
36.
(2, 7) and (-4, 4)
37.
(-1, 2) and (4, -23)
38.
(4, -1) and (-8, -10)
39.
(0, 11) and (-7, -3)
40.
(1, 27) and (-2, 12)
Worksheet adapted from 2007 Holt, Rinehart and Winston Algebra 1 Book 5-7 Point-Slope Form
345
(2-4)A Writing Linear Equations
(2-4)A
41. Science At higher altitudes, water boils at lower temperatures. This relationship between altitude and boiling point is linear. The table shows some altitudes and the corresponding boiling points. Write an equation in slope-intercept form that represents this linear function. Then find the boiling point at 6000 feet.
Science
Boiling Point of Water Altitude (ft)
Temperature (°F)
1000
210
1500
209
3000
206
The tables show linear relationships between x and y. Copy and complete the tables. As altitude increases, the amount of breathable oxygen decreases. At elevations above 8000 feet, this can cause altitude sickness. To prevent this, mountain climbers often use tanks containing a mixture of air and pure oxygen.
42.
44.
x
-2
y
-18
0
43.
7 12
27
x
-4
1
y
14
4
0 -6
/////ERROR ANALYSIS///// Two students used point-slope form to find an equation that describes the line with slope -3 through ( -5, 2). Who is incorrect? Explain the error.
rr* f ! q q*" r+ ,! q."
rr* f ! q q*" r+ ,T q! ."V r+ ,! q ."
45. Critical Thinking Compare the methods for finding the equation that describes a line when you know • a point on the line and the slope of the line. • two points on the line. How are the methods alike? How are they different? 46. Write About It Explain why the first statement is false but the second is true. • All linear equations can be written in point-slope form. • All linear equations that describe functions can be written in point-slope form. 47. Multi-Step The table shows the mean combined (verbal and math) SAT scores for several different years. 49. Which equation describes the line through (-5, 1) with slope of 1? +1= x-5 YearsySince 1980 + 5 = x -Score 1 MeanyCombined
0
5
994
1009
) y - 110= -5(x - 117 y -1001 1=x+5
21
1016
1020
50. a.A line contains (4,plot 4) and (5, data 2). What are the slope and Make a scatter of the and add a trend line to y-intercept? your graph. -2 ;line y-intercept = 2 the slope and y-intercept, slope = -2;and y-intercept 12 b. Useslope your= trend to estimate write an= equation in slope-intercept form. slope = 1.2 ; y-intercept = -2 slope = 12; y-intercept = 1.2 c. What do the slope and y-intercept represent in this situation?
CHALLENGE EXTEND 49. Which equationAND describes the line through (-5, 1) with slope of 1?
51. A linear has y-intercept as x +y4y 8 its-graph y +function 1 = will x - prepare 5 the same -= 1 =and -5 1)364.contains the 48. This problem you for the Multi-Step Test Prep on(xpage point (2, 7). Find the slope and y-intercept. y + 5 is = walking x - 1 from his house to his friendy Sharon’s -1=x+ 5 a. Stephen house. When he is 12 3 __ __ 52. Write the away, equation of a line in watch. slope-intercept contains , 1 and hasand the blocks he looks at his He looks form againthat when he is 8 blocks away 4 2 50. A line contains (4, 4) and (5, 2). What are the slope and y-intercept? same slope the line described by yWrite + 3x two = 6.ordered pairs for these data in the finds thatas 6 minutes have passed. slope = -2 ; y-intercept = 2 slope = -2; y-intercept = 12 form (time, blocks). 53. Write the equation of a line in slope-intercept form that contains - __12 , - __13 and 1 __12 , 1 . slope = 1.2 ; y-intercept = -2 b. Write a linear equation for these two points. slope = 12; y-intercept = 1.2 c. What is the total amount of time it takes Stephen to reach Sharon’s house? SPIRAL REVIEW Explain how you found your answer. CHALLENGE AND EXTEND Solve each compound inequality and graph the solutions. (Lesson 3-6) 51. A linear function has the same y-intercept55. as xm+-4y5 = and its graph the 54. -4 ≤ x + 2 ≤ 1 > 8-7 AND m + 1 contains <2 point 2, 7 . Find the slope and y-intercept. ) ( Chapter 5 Linear Functions Graph each function. 4-4) 52. Write the equation(Lesson of a line in slope-intercept form that contains __34 , __12 and has the slope +53x = 6. 56. same y=x3 as the line described 57. y =byx 2y+ 58. y = 2x
( )
(
346
d-12 346
)
(
)
)
(
)
( )
(
53. Write the equation of a line in slope-intercept form that contains - __12 , - __13 and 1 __12 , 1 . Write the equation that describes each line in slope-intercept form. (Lesson 5-6) 59. slope = 3, y-intercept = -5
SPIRAL REVIEW
60. slope = -2, the point (2, 4) is on the line11/1/05
Worksheet adapted frominequality 2007 Holt, Winston Algebra Solve each compound andRinehart graph theand solutions. (Lesson 3-6) 1 Book 54. -4 ≤ x + 2 ≤ 1
55. m - 5 > -7 AND m + 1 < 2
6:22:24 PM
(2-4)A Writing Linear Equations 1.
3.
5. y - 5 = -4(x - 1) 7. y = - 1/3x + 7 9. y = 1/3x 11. y = 3x - 13 13. y = -x 15. y = - 1/3x + 4/3 17. y = -x + 15 19. y = 1/5x + 3 ; 9 ft 21.
23. 25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 49. 55. 59.
11/1/05 6:22:22 PM
y - 5 = 2/9(x + 1) y - 8 = 8(x - 1) y - 7 = 3(x - 4) y = - 2/7x + 1 y = - 1/4x y = - 5x + 13 y = 1/7x + 7 y = - 5x - 3 y = 2x + 11 y = - 1/500x + 212 ; 200° F 6;6 D m > -2 and m < 1 y = 3x - 5
