:
Alg 1H
Write the equations for the horizontal and vertical lines that pass through the given point.
1.
(3, 10) Horiz._________ Vert._________ 2.
(0, 8) Horiz._________ Vert._________
Use the slope formula to find the slope of the line that passes through the two points.
3.
(2, 3) , (4, 6) 4.
(3, 10) , (3, 4) 5.
(־5, 2) , (2, ־4) 6.
(5, 6) , (1, 6) 7.
(3, 7) , (9, 5)
Graph the following equations.
8.
y = –3x + 2 9.
y =
1
2 x – 3
Sketch the line with the given slope through the given point.
10.
(0, 5), m =

1
11.
(־1, ־3), m =
1
4 2
Write each equation in slope-intercept form and graph.
3
12.
x + y = 5 13.
y –
2 x + 3 = 0
Find the x and y-intercepts of the line.
Write your answers as coordinate points and label them with the name of the intercept.
14.
2x + 5y = 20 15.
y = 8x – 4 16.
5
4 x

3
2 y

9
17. What is the slope of a line that contains the point (2, -3) and has the same x-intercept as x +
5y = 8?
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
18.
If y = – 4 when x = 1, find y when x = 3.
19.
If y = 8 when x = 6, find y when x = 9.
20. If y = 35 when x = 14, find y when x = 41.
Find the s l o p e and y - i n t e r c e p t of the lines.
21. 2x + 4y = 1 22.
y = –7 23. 4y

7x = 5
For 24 – 27 write a linear equation in Slope – Intercept Form.
24.
Passes through the point ( 3 , ־ 4 ) with a slope of
3
2
25.
Passes through the points ( 1 , ־ 7 ) and ( 3 , ־ 15) .
26. Passes through the points ( 7 , 2 ) and ( 4 , 2 ) .
27.
Passes through the points ( ־ 5 , ־ 6 ) and ( 2 , 8 ) .
.

Find the value of x so the line that passes through the pair of points and has the given slope:
28.
( 5 , ־ 9 ) and ( x , ־ 3) , m =

4
5
29. The cab fare varies directly with the number of miles driven, as shown in the table.
Miles Driven 1 2 3 4 5
Cab Fare $1.25 $2.50 $3.75 $5.00 $6.25
Write and graph an equation that relates the cab fare, y, to the miles driven, x.
30.
The monthly telephone bill consists of $24 service charge plus $1.20 per call. Write an equation in slope-intercept form for the total monthly bill if x represents the number of calls made in a month. Then graph the equation. If your bill last month was $230.40 use your equation to find the number of calls you made.
Page 212, # 1 – 16.

T-1 Rev A Review for Trimester 1 Benchmark Exam Alg 1H
Do in your spiral and show all support work!
1. Evaluate the expression 72x + 15 – x 3 when x = ־ 2.
2. Is x = – 6 a solution of the equation 23 – 3x = – 4x + 17?
Simplify the expressions:
3. 3(x – 5) – 4(x + 3x) 4. 2(x – 8) – (x – 7) 5.
30 
3
21 x
Solve the equations:
6. 5x – 7(3 – 2x) = 36 7.
1
3 x = 7 –
2
3 x 8. x + 23 = 3(2x + 1)
9. 14 – (6 – 3c) = 4c – c 10. 3y – 2(y + 19) = 9y – 3(9 – y) 11. 2(a – 8) + 7 = 5(a + 2) – 3a - 19
12. Solve the equation for b: 12ab + 7b = 5a.
13. Solve the equation for a: 12ab + 7b = 5a.
14. Find the slope and y-intercept of the line 4x – 7y = 14.
15. Find the slope of the line containing the points ( ־ 3, 8) and (5, 2).
16. Sketch the graph and label the intercepts of the equation 5x – 3y = 30.
17. Make a table of values for y =
2
3 x – 5. Use the values – 6, – 3, 0, 3, 6, 9 for x.
18. Write the equation of the line passing through the points (3, 7) and (7, 7).
19. What is the slope of the line from your equation in problem #18?
20. In 1994 a company had 36 employees. By 1998 the company had grown to 108 employees. Find the average rate of change and label your answer with units.
21. Write in slope-intercept form and sketch the line. 3x – 2y = 12.
22. Write in slope-intercept form the equation of the line that passes through (4, ־ 1), and (0, 3).
23. Write in slope-intercept form the equation of the line that passes through ( ־ 5, 4), and (-5, ־ 2).
24. Write the equation y = 
6
5 x +
3
2
in standard form with integer coefficients.
25. Write in point-slope form the equation of the line that passes through the point (4, ־ 9) with a slope of
1
5
.
26. Identify the hypothesis and conclusion of the statement, then rewrite the statement in “ifthen” form. “A quadrilateral with 4 equal sides is a rhombus.”

27. Find a counterexample for the statement: If a and b are real numbers, (a + b) 3 = a 3 + b 3 .
28. Identify each as rational or irrational numbers: 93
8
7

144
3
125
36
29. Solve the proportion: x
2
 3
 x
5
 1
.
30. Does the pair of ratios form a proportion?
1 .
5
9
,
1
6
31. Find the final price of the item. Printer $255.00 discount 30% tax 5.5%
32. Is the relation a function? (-4, 3), (1, -5), (7, 6), (9, 6), (1, 5)
33. If f(x) = 2x 2 + 1, find f(3n).
34. Identify the domain and range of the function. (1, 4), (2, -2), (3, -6), (-6, 3), (-3, -6).
35. Find the value of r so that the line through (8, r) and (4, 5) has a slope of -4.
36. Find the value of r in (4, r) , (r, 2) so that the slope of the line containing them is 
5
3
.
37. Find the slope-intercept form of an equation for the line that passes through (-1, 2) and is parallel to the equation y = 2x – 3.
38. Find the slope-intercept form of an equation of the line perpendicular to the line x – 3y = 5 and passing through the point (0, 6).
39. The table of ordered pairs shows the coordinates of two points on the graph of a function.
What is the equation that describes the function? x y
-2 2
4 -1
40. Write the equations of the horizontal and vertical lines that pass through the point (-2, -7).

Do in spiral and show all support work!
1) Which is an example of the Distributive Property?
A) (5 – 2) + 3 = (-2 + 5) + 3 B) 5(2 – 3) = 5
·
2 – 5
·
3
C) (5 – 2) + 3 = 5 + (-2 + 3) D) (5 – 2) – 3 = 0
2) Which equation is equal to 2y = 4 + 3(8 – 2 2 )
A) 2y = 16 B) 2y = 24 C) 2y = 112 D) 2y = 84
3) What is the solution of 4(3x – 2) – (4x – 3) = 11 A) 1 B)
1
1
4
C)
4) Which set of numbers is closed under the operation of division?
A) integers B) rational numbers, except division by 0
4
3
C) irrational numbers D) none of the above
5) Which property makes it easier to evaluate the expression (87 • 25) • 4 mentally?
A) Commutative Property B) Associative Property
D) 2
C) Distributive Property D) Multiplicative Inverse
6) For which set of numbers is the inequality x 2  x
true?
A) real numbers B) rational numbers
C) integers D) all of the above
7) Which is a counterexample for the conjecture, “the difference between two negative integers is always positive?”
A) -7 – 2 = -9 B) 7 – 4 = 3 C) -5 – (-2) = -3 D) -5 – (-7) = 2
8) What is the domain of the function given by
A)

7

B)

 1 , 2 , 5 , 7

C)

   
 1 , 2      
?
2 , 3 , 6 , 7

D)

 1 , 3 , 5 , 6

9) What is the opposite of the reciprocal of

4
5
? A)
4
5
B)

5
4
C)
5
4
D)

4
5
10) What is the solution for the equation 3(y + 2) – 4(2y – 1) = 8
A)

9
5
B)

2
5
C)
2
5
D)
9
5
11) Adult tickets for the school concert cost $5 and student tickets cost $3.50. The school sold $2162.50 worth of tickets. If 120 more students than adults attended the concert, how many students attended the concert?
A) 205 B) 315 C) 325 D) 455
12) What is the solution for the equation?
A)
363
50
B) 3
4
5 x
C)
3
2

7
5 x 
33
10
D)
2
3
13) A movie discount pass, which has an annual fee of $50, allows a moviegoer to pay $6 per movie. If a movie ticket normally costs $8.50, how many movie tickets must a moviegoer buy to make the discount pass a bargain?
A) at least 25 B) more than 20 C) 20 or fewer D) more than 19

14) What is the solution for the equation? 2.96 = 0.08(x – 4)
A) 4.1 B) 33 C) 41 D) 87
15) The Morena family drove to Yosemite National Park in 3 hours. On the way home, they averaged 15 miles per hour less and the trip took 4 hours. How far from Yosemite National Park do they live?
A) 60 miles B) 180 miles C) 45 miles D) 210 miles
16) What is the value of m to the nearest tenth when 0.45m – 0.7m = 50.55
A) -202.2 B) -144.4 C) 44.0 D) -20.2
17) It would take each member of the 3-member dance committee 5 hours to inflate all the balloons alone. How long would it take them to inflate the balloons together?
A)
1
1
3
hours B)
1
1
2 hours C)
1
2
3 hours D)
1
3
4 hours
18) What is the solution for the equation? n 
3
5

2 n
4
 1

3 n 
6
4
A)
25
4
B)
27
8
C)
25
8
D)

25
4
19) Your brother starts out 10 minutes before you on a bike path and rides at a rate of 9 miles per hour.
If you ride at a rate of 12 miles per hour, how long will it take you to catch up to him?
A)
1
4 hour B)
1
2 hour C)
2
3 hour D)
3
4 hour
20) Which relation is a function?
A)
C)

        
3 ,
1
,
, 0 ,
3
2 , 2 ,
2 ,
3
,
, 3 , 2

B)

D)


       
5 , 2 , 5 , 3 , 2 , 2 , 3 ,


21) In the equation t = 2000p, where tons are a function of pounds, what does t represent?
A) the dependent variable B) the independent variable
C) the intercept D) the slope
22) What is the y-intercept for the equation? 6x – 2y = -4
A) -2 B)

2
3
C) 2 D)
1
2
23) Which statement is true about the relationship between the domain ( D ) and the range ( R ) of a function?
A) For every element in D , there is only one corresponding element in R .
B) For every element in R , there is only one corresponding element in D .
C) There must be the same number of elements in D and R .
D) The elements of D are the dependent variables.
24) Which equation represents the line that passes through the point (-2, 3) with a slope of
3
4
?
A) 3x – 4y = 17 B) 4x + 3y = 1 C) 2x + 3y = 5 D) 3x – 4y = -18
25) Which situation is most likely represented by the graph?
A) amount of tip money earned by a waiter every night
B) price of a stock on the stock market
C) wages paid to an hourly employee at a factory
D) daily commissions earned by a real estate agent
26) What is the x-intercept for the equation?5x – 2y = 10
A) 2 B) -2 C) -5 D) 5
27) What is the slope of the line? 2x + 3y = 6
A) 2 B)

3
2
C)

2
3
D) -2
Money
Time

28) Which point is on the line? 5x – 3y = -1
A) (1, 2) B)
2
3
C) (4, 7) D) all of the above
29) Which ordered pair represents the x-intercept of the line? 4x – 3y = 12
A) (0, 3) B) (3, 0) C) (0, -4) D) (-4, 0)
30) What is the equation of the line that passes through the point (3, 2) and has a slope of
A) y  2 
2
3
 x  3 
B) y  3 
2
3
 x  2 
C) y
31) Which point is a solution to the inequality? 3x + 2y < 6
 2  
2
3
 x  3 
D) y  3

2
3
?
 
2
3
 x  2 
A) (3, 2) B) (-1, 5) C) (0, 3) D) (-1, 2)
32) What is the equation of the line that passes through the point (1, 4) and is parallel to the graph of 2x – y = 9?
A) 2x – y = -2 B) 2x – y = 4 C) 2x + y = 6 D) x + 2y = 9
33) Which ordered pair represents where the graph of 5x – 2y = 10 intersects the y-axis?
A) (0, -5) B) (-5, 0) C) (0, 2) D) (2, 0)
34) On a scatter plot, the x-axis represents the latitude from the equator to the North Pole and the y-axis represents the average temperature.
Which type of correlation is represented?
A) positive correlation
B) negative correlation
C) no correlation
Temperature
D) none of the above
35) The graph of a linear function contains the
following data points. What is the slope of the line?
A)
1
25
B)
1
5
C) 5 D) 25
Latitude
Number of cars
5
10
15
20
25
Car wash
$25
$50
$75
$100
$125
36) Which point is not on the line? 6x – 8y = -2
A) (1, 1) B)
1
2
C) (2, 2) D) (0.5, 0.625)
37) Which point is on the line? y 
3
4 x  5
A) (4, 7) B) (4, -2) C) (0, 5) D) (-5, 0)
38) What is the equation of the line that passes through the point (3, -1) and is perpendicular to the line
2x – 4y = 8?
A) 2x – y = 7 B) x + 2y = 1 C) 2x + y = 5 D) x – 2y = 5

For 1 – 9, define variables, write a verbal sentence, write an equation, and solve. Show all support work.
1.
Kathy started a savings account with $50. After 7 months she had $260 in the account. When did she have exactly $800 in the account?
2.
Erik has 16 more nickels than dimes in his wallet. If he has a total of $3.50 in nickels and dimes, find the number of each type of coin.
3.
The length of a rectangle is five less than twice its width. If the perimeter is 68 cm, find the dimensions of the rectangle.
4.
The sum of four consecutive even integers is 540. Find the integers.
5.
Tickets for a play cost $6 for adults and $3 for students. A total of 407 tickets worth $2037 were sold. How many adult tickets were sold?
6.
A grocer has dried apples selling for $1.50/lb. and dried bananas selling for $1.25/lb.
How many pounds of each did he use to make a mixture of 10 pounds that will sell for
$1.30/lb.?
7.
A small city park has a rectangular-shaped lawn surrounded on all sides by a border of crushed gravel that is 2 meters wide. The lawn is 5 meters longer than it is wide. The area of the crushed gravel border is 364 m 2 . Find the dimensions of the lawn.
8.
Two trains left Chicago, one traveling east at 30 mph and the other traveling west at
40 mph. After how many hours were the two trains 245 miles apart?
9.
A car going 50 mph left Thousand Oaks, heading toward South Bend, Indiana. Three hours later a second car going 70 mph left, traveling on the same road. How many hours will it take for the second car to overtake the first car?
Solve:
10. Y varies directly as x. If y = 7 when x = 5, find x when y = 20.
11. Charles’s Law states that, at a constant pressure, volume of a gas V varies directly as its temperature, T. A volume of 4 cubic feet of a certain gas has a temperature of 200°. Find the volume of the same gas at 250°.
Solve:
12. x 
3
2 x

3
4 x

5
6
13. m 
10
6
 m
15

2
5
14.
3 x  4
5
 x 
2
3
15. y 
2
3
 y 
6
3
 4
16. 2[5(y + 3) – (y + 1)] = 3(1 + y) 17. x
6
 x 
5
3
 1