Deck 1: Preliminaries

Question 1

Writing the equation in the slope intercept form, find the slope of the line.

A)
B)
C)
D)
E)

Answer 1

Question 2

Find an equation of the line in general form that passes through the point (5, 2) and is perpendicular to the line 8x + 3y - 4 = 0.

A)
B)
C)
D)
E)

Answer 2

Question 3

Writing the equation in the slope intercept form, find the slope of the line.

A)
B)
C)
D)
E)

Answer 3

Question 4

Determine whether , , and lie on a straight line.

A)yes
B)no

Question 5

Use the intercept form of an equation of a line to find an equation of a line with the -intercept 9 and the -intercept 4.

A)
B)
C)
D)
E)

Question 6

Determine whether the points A(-2, 9), B(4, -1), and C(7, -6) lie on a straight line.

A)no
B)yes

Question 7

Find an equation of the line that parallel to the y-axis and 4 units left of it.

A)
B)
C)
D)
E)

Question 8

Use the intercept form of an equation of a line to find an equation of a line with the -intercept and the -intercept .

A)
B)
C)
D)
E)

Question 9

Using data compiled by the Admissions Office at Faber University, college admissions officers estimate that 55% of the students who are offered admission to the freshman class at the university will actually enroll.If the desired freshman class size for the upcoming academic year is 1,650 students, how many students should be admitted?

A)3,600
B)3,000
C)1,800
D)2,700
E)3,900

Question 10

Find an equation of the line in general form that passes through the point (- 9, 7) and is parallel to the line 8x - 9y - 7 = 0.

A)
B)
C)
D)
E)

Question 11

Find an equation of the line that has slope m = 7 and y-intercept b = 1.

A)
B)
C)
D)
E)

Question 12

Find an equation of the line that passes through the point (4, -5) and has the indicated slope m = 7.

A)
B)
C)
D)
E)

Question 13

Given that the point lies on the line , find k.

A)
B)
C)
D)
E)

Question 14

Given that the point lies on the line , find k.

A)
B)
C)
D)
E)

Question 15

Metro Department Store's annual sales (in millions of dollars) during the past 5 yr were Derive an equation of the line L through the points corresponding to the first and fifth years.

A)
B)
C)
D)
E)

Question 16

Write the equation in the slope-intercept form and then find the slope and -intercept of the corresponding line.

A)
B)
C)
D)

Question 17

If the line passing through the points and is parallel to the line passing through the points and , what is the value of a?

A)
B)
C)
D)
E)

Question 18

Find an equation of the line that parallel to the x-axis and 4 units below it.

A)
B)
C)
D)
E)

Question 19

If the slope of the line is negative, then the slope of a line perpendicular to may be positive or negative?

A)negative
B)positive

Question 20

Find an equation of the line that passes through the points (9, 3) and (11, 21).

A)
B)
C)
D)
E)

Question 21

If the line passing through the points and is parallel to the line passing through the points and , what is the value of a? __________

Question 22

Find the slope of the line shown in the figure.

A)
B)
C)
D)
E)

Question 23

If the line passing through the points (2, a) and (4, -8) is parallel to the line passing through the points (5, 5) and (-1, a + 13), what is the value of a?
a = __________

Question 24

Given that the point lies on the line , find k. __________

Question 25

Given the equation 2x + 7y = 4, if x decreases by 4 units, what is the corresponding change in y?

A)
B)
C)
D)
E)

Question 26

Determine whether the line through each pair of points is parallel. A(1, -3), B(-1, -11) and C(1, 5), D(-1, -3).

A)parallel
B)not parallel

Question 27

Use the intercept form of an equation of a line to find an equation of a line with the -intercept 9 and the -intercept 8.

Question 28

Given the graph of a line, which of the following statements is true?

A)The slope of the line is negative, and its y-intercept is positive.
B)The slope of the line is negative, and its y-intercept is negative.
C)The slope of the line is positive, and its y-intercept is negative.
D)The slope of the line is positive, and its y-intercept is positive.
E)The slope of the line is zero.

Question 29

If the line passing through the points (1, a) and (3, -6) is parallel to the line passing through the points (6, 8) and (0, a + 14), what is the value of a?

A)-6
B)-10
C)-3
D)-4
E)-7

Question 30

Find the slope of the line that passes through points and m = __________

Question 31

Find the slope of the line shown in the figure.

Question 32

Find an equation of the horizontal line that passes through (-5, -4).

A)
B)
C)
D)
E)

Question 33

Find the slope of the line that passes through points and m = __________

Question 34

Find the slope of the line shown in the figure. m = __________

Question 35

Find the slope of the line shown in the figure.

A)
B)
C)
D)
E)

Question 36

Determine whether the line through each pair of points is perpendicular. A(4, 10), B(9, 7) and C(-3, -6), D(0, 0)

A)perpendicular
B)not perpendicular

Question 37

Find the slope of the line that passes through points and

A)5
B)4
C)1
D)2
E)-2

Question 38

Find an equation of the vertical line that passes through (1, 8).

A)
B)
C)
D)
E)

Question 39

Match the statement with one of the graphs. Choose the correct letter for each question.

1.The slope of the line is undefined.
2.The slope of the line is positive, and its y-intercept is negative
3.The slope of the line is zero
4.The slope of the line is positive, and its y-intercept is positive

a.

b.

c.

d.

Question 40

Find the slope of the line that passes through points and

A)6
B)1
C)3
D)2
E)7

Question 41

Find an equation of the line that passes through the point (9, 7) and is perpendicular to the line
5x + 3y - 4 = 0.

Question 42

Determine whether the points A(-3, 7), B(2, -3), and C(9, -16) lie on a straight line.Answer yes or no.

Question 43

Find an equation of the line that has slope m = 5 and y-intercept b = 2.

Question 44

Determine whether the line through each pair of points is perpendicular.Answer perpendicular or not perpendicular.
A(4, 10), B(7, 7) and C(-4, -8), D(1, -3)

Question 45

Determine whether , , and lie on a straight line.Answer yes or no.

Question 46

Find an equation of the line that is parallel to the x-axis and 7 units below it.

Question 47

Find the coordinates of the points that are units away from the origin and have an x-coordinate equal to .

A) and
B) and
C) and
D)
E)

Question 48

Determine whether the statement is true or false.
The point ( -n, m) is symmetric to the point (n, m) with respect to the y-axis.

Question 49

Find an equation of the line that passes through the points (6, 7) and (8, 23).

Question 50

Determine whether the line through each pair of points is parallel.Answer parallel or not parallel.
A(4, -1), B(-3, -36) and C(4, 4), D(-1, -6)

Question 51

Ivan wishes to determine which antenna he should purchase for his home.The TV store has supplied him with the information: Ivan wishes to receive Channel 17 (VHF) that is located 22 mi east and 41 mi north of his home and Channel 38 (UHF) that is located 24 mi south and 44 mi west of his home.Which model will allow him to receive both channels at the least cost? (Assume that the terrain between Ivan's home and both broadcasting stations is flat.)

A)Model B
B)Model A
C)Model D
D)Model C

Question 52

If the slope of the line is positive, then the slope of a line perpendicular to may be positive or negative?

Question 53

Determine whether the statement is true or false.
The circle with equation lies inside the circle with equation provided

Question 54

Find an equation of the line that passes through the point (7, -9) and has the slope m = 6.

Question 55

Ship A leaves port sailing north at a speed of 25 mph.A half hour later, ship B leaves the same port sailing east at a speed of 16 mph.Let t (in hours) denote the time ship B has been at sea.Find an expression in terms of t giving the distance between the two ships and use this expression to find the distance between the two ships 2 hours after ship A has left port.Round the answer to the nearest tenth.

A)62.5 mi
B)54.0 mi
C)54.5 mi
D)55.5 mi
E)53.5 mi

Question 56

Find the distance between the points and .

A)
B)
C)
D)
E)

Question 57

Plot point (-4, -7) on the set of coordinate axes.

A)
B)
C)
D)
E)

Question 58

A furniture store offers free setup and delivery services to all points within a 23-mi radius of its warehouse distribution center.If you live 19 mi east and 14 mi south of the warehouse, will you incur a delivery charge?

A)Yes
B)No

Question 59

Find an equation of the line that passes through the point (- 6, 5) and is parallel to the line
2x - 3y - 4 = 0.

Question 60

Find an equation of the horizontal line that passes through (-6, -7).

Question 61

Find an equation of the circle that satisfies the conditions. Center and passes through .

A)
B)
C)
D)
E)

Question 62

Refer to the following figure.Which points have negative y-coordinates?

A)A, B, D
B)F, A, E, C
C)G, D, B
D)F, A, D, G
E)E, B, C

Question 63

Refer to the following figure.Which points have a negative x-coordinate and a negative y-coordinate?

A)A, C, B
B)G, C
C)E, A
D)B
E)D, F

Question 64

Refer to the following figure.Which point has an x-coordinate that is equal to zero?

A)F
B)A
C)B
D)E
E)C

Question 65

Refer to the following figure.Which points have a positive x-coordinate and a negative y-coordinate?

A)D
B)A, B
C)F, G
D)E
E)C, A, B

Question 66

Find an equation of the circle with center at (a, a) and radius 3a.

A)
B)
C)
D)
E)

Question 67

If the equation of circle is .Find the radius of the circle with centre at the origin.

A)
B)
C)
D)
E)

Question 68

A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A.If the cities are located as shown in the following figure, find the total distance covered on the tour. __________

Question 69

Refer to the following figure.Which point has coordinates (-3, 4)?

A)A
B)B
C)G
D)D
E)C

Question 70

Find the distance between the points (2, 2) and (4, 7).

A)
B)
C)
D)
E)

Question 71

Find an equation of the circle with radius 5 and center (-3, 2).

A)
B)
C)
D)
E)

Question 72

Refer to the following figure and determine the coordinates of point and the quadrant in which it is located.

A)(4, 5) and first quadrant
B)(-3, 5) and first quadrant
C)(4, 5) and third quadrant
D)(3, 3) and third quadrant
E)(3, 3) and first quadrant

Question 73

The circle with equation lies inside the circle with equation means.

A)
B)
C)
D)
E)these curves are intersecting

Question 74

Find an equation of the circle with center at the origin that passes through (4, 5).

A)
B)
C)
D)
E)

Question 75

Find the coordinates of the points that are 13 units away from the origin and have a y-coordinate equal to -5.

A) and
B) and
C) and
D) and
E) and

Question 76

Refer to the following figure.What are the coordinates of point B?

A)(4, 10)
B)(-3, 3)
C)(10, -6)
D)(14, 14)
E)(-9, -13)

Question 77

Refer to the following figure.Which points have a negative x-coordinate and a positive y-coordinate?

A)E
B)A, B
C)D
D)C, A, B
E)F, G

Question 78

Refer to the following figure.Which point has a y-coordinate that is equal to zero?

A)G
B)B
C)E
D)C
E)A

Question 79

Refer to the following figure.What are the coordinates of point A?

A)(-2, 0)
B)(2, 2)
C)(2, 0)
D)(-2, -2)
E)(2, -2)

Question 80

Plot point ( , ) on the set of coordinate axes.

A)
B)
C)
D)
E)