Section 2.1 Intercepts and symmetry
#1 – 4: Find the x and y-intercepts
1)
2)
3)
Section 2.1 Intercepts and symmetry
4)
#5-18: Find the x and y-intercepts.
5) 3x - 6y = 24
6) 2x + 4y = 12
7) y2 = x + 9
8) y2 = x + 16
9) y = 3x2 + 4x – 7
10) y = 2x2 + 3x – 9
11) x = 3y2 – 7y + 2
12) x = 2y2 + 9y + 9
𝑥+1
13) 𝑦 = 3𝑥−6
15) 𝑦 =
𝑥 2 −5𝑥+6
𝑥+1
17) x2 + y2 = 16
14) 𝑦 =
16) 𝑦 =
2𝑥+10
𝑥−5
2𝑥 2 +5𝑥+2
𝑥−3
18) x2 + y2 = 25
Section 2.1 Intercepts and symmetry
#19 – 30, plot each point. Then plot the point that is symmetric to it with respect to (a) the xaxis; (b) the y-axis; (c) the origin
19) (1,2)
20) (2,4)
21) (-1, 3)
22) (-2, 5)
23) (4, - 5)
24) (5, -1)
25) (-3, -2)
26) (-2, - 7)
27) (5, 0)
28) ( 4, 0)
29) (0, -2)
30) (0, -3)
#31 – 38. Determine whether the graph is symmetric to the x-axis, y-axis, the origin, or none of
these.
31)
32)
Section 2.1 Intercepts and symmetry.
33)
34)
35)
Section 2.1 Intercepts and symmetry.
36)
37)
38)
Section 2.1 Intercepts and symmetry.
#39 – 50: determine the type of symmetry the graph of the equation has (if any). Make sure to
perform the appropriate test to confirm your answer.
39) y2 = x – 4
40) y2 = x + 1
41) x2 + y = 8
42) x2 + y = 2
43) y = 2x3
44) y = 3x3
45) y = x2 + 6x + 5
46) y = x2 – 3x – 4
47) x2 + 2 = y
48) x2 + 6 = y
49) y2 + x = 5
50) y2 – 3 = x
Section 2.2 lines
#1-6: Plot the points on a graph then find the distance between the points.
1) (3, 4) and (6, 8)
2) (1, 2) and ( 4, 6)
3) (2, -5) and (4, -1)
4) (-3, 5) and (-1, 1)
5) (7, 3) and (4, 3)
6) (5,1) and (5, 2)
#7 – 12: Plot the points on a graph, then the midpoint of the line segment that connects the
points.
7) (3, 4) and (6, 8)
8) (1, 2) and ( 4, 8)
9) (2, -5) and (4, -1)
10) (-3, 5) and (-1, 1)
11) (7, 3) and (4, 3)
12) (5,1) and (5, 2)
#13 – 20: Determine the slope of the line the connects the two points.
13) (3, 4) and (6, 8)
14) (1, 2) and ( 4, 14)
15) (2, -5) and (4, -1)
16) (-3, 5) and (-1, 1)
17) (7, 3) and (7, 2)
18) (5,1) and (5, 2)
19) (3,5) and (4,5)
20) (6,2) and (-7,2)
#21 – 30: sketch a graph of the following lines. Label at least 4 points.
2
21) 𝑦 = 3 𝑥 − 5
23) 𝑦 =
2
3
𝑥
1
22) 𝑦 = 4 𝑥 − 2
1
24) 𝑦 = 4 𝑥
25) y = 3x - 2
26) y = 6x + 1
27) 3x + 2y = 10
28) 4x + 5y = 10
29) 2x + 3y = 0
30) 5x – 2y = 0
Section 2.2 lines
#31 – 38: Find the x and y-intercepts then sketch a graph (it will be enough to label two points
on your graph)
31) 2x + y = 12
32) 3x + y = 15
33) 4x + 2y = 15
34) 3x – 6y = 9
35)
37)
1
2
𝑥 − 3𝑦 = 2
2
36)
2
𝑥 + 5𝑦 = −2
3
38)
2
1
2
𝑥−𝑦 =4
𝑥 − 2𝑦 = 5
3
7
#39 – 56, find an equation for the line with the given properties. Express your answer in slope
intercept form.
39) Slope = 4; containing the point (5, -2)
2
40) Slope = -2; containing the point (-4,1)
1
41) Slope = 3; containing the point (6,5)
42) Slope = 3; containing the point (12, -2)
43) Slope 5; y-intercept = -2
44) Slope = -4; y-intercept = -1
45) Parallel to the line y = 3x + 6; containing the point (4,1)
46) Parallel to the line y = 3x – 2; containing the point (-5,1)
4
47) Parallel to the line 𝑦 = 9 𝑥 + 3; containing the point (0,1)
48) Parallel to the line 𝑦 =
−2
3
𝑥 − 4; containing the point (5,1)
49) Perpendicular to the line y = 3x + 6; containing the point (4,1)
50) Perpendicular to the line y = 3x – 2; containing the point (-5,1)
4
51) Perpendicular to the line 𝑦 = 9 𝑥 + 3; containing the point (0,1)
52) Perpendicular to the line 𝑦 =
−2
3
𝑥 − 4; containing the point (5,1)
53) Passing through the points (3,1) and (4,5)
54) Passing through the points (5,2) and (6, 3)
55) Passing through the points (-4,5) and (-2,1)
Section 2.3 circles
The Standard Form of the Equation of a Circle
(h, k) is the center
r is the radius
(x, y) is any point on the circle
#1-8: Write the standard form of the equation of the circle with the given radius (r) and center
(h,k) then sketch a graph of the circle.
1) r = 2 (h,k) = (3, -1)
2) r = 4 (h,k) = (5, -4)
3) r = 3 (h,k) = (-4,1)
4) r = 5 (h,k) = (-6,3)
1
1
5) r = 2 (h,k) = (-3,-2)
6) 𝑟 = 3 (h,k) = (1, 3)
7) r = 5 (h,k) = (0,2)
8) r = 8 (h,k) = (0,3)
Section 2.3 circles
#9-18: rewrite so that the equation is written in the standard form of a circle. Then sketch a
graph.
9) x2 + y2 -6x + 2y + 9 = 0
10) x2 + y2 -2x + 4y – 4 = 0
11) x2 + y2 – 4x – 6y = -4
12) x2 + y2 + 2x + 6y = 6
13) x2 + y2 – 6y = 16
14) x2 + y2 – 4y = 21
15) x2 – 6x + y2 = 40
16) x2 – 4x + y2 = 5
17) 3x2 + 3y2 – 12 = 0
18) 2x2 +2y2 + 8x + 6 = 0
#19 - 26: Find the standard form of the equation of each circle. It may help to sketch a graph of
the circle before you start your algebra.
19) Center (-2, 3) contains the point (1, 7)
20) Center (1, 5) contains the point (5, -3)
21) Center (5, 2) tangent to the y-axis
22) Center (4,1) tangent to the y-axis
23) Has a diameter with endpoints (1,4) and (-3,2)
24) Has a diameter with endpoints (1, 5) and (3, 11)
25) Has a diameter with endpoints (0,6) and (4,6)
26) Has a diameter with endpoints (5, 0) and (5, 4)
Section 2.4 Variation
#1 - 14: Write a variation model. Use k as the constant of variation.
1) W varies directly as the square of x
2) A varies directly as the square root of b
3) Y varies inversely as the cube of x
4) Z varies inversely as the square of y.
5) Q is directly proportional to the square of x and inversely proportional to the cube of y.
6) W is directly proportional to the square root of x and inversely proportional to y.
7) M varies jointly as the square of x and the cube of y.
8) B varies jointly as x and the square root of y.
9) The distance (D) an object falls is directly proportional to the square of the time (T) it falls.
10) The monthly payment (P) on a mortgage varies directly as the amount borrowed (B)
11) The maximum weight (W) that can be supported by a two by four piece of wood varies
inversely as its length (L).
12) The demand (D) for candy at a movie theater is inversely related to the price (p).
13) The volume (V) of an enclosed gas varies directly as the temperature (T) and inversely as
the pressure (P).
14) The diameter (D) of the largest particle that can be moved by a stream varies directly as
the square of the velocity (V) of the stream.
#15 - 20: Find the constant of variation, k.
15) y varies directly as the square of x and y is 45 when x is 3.
16) M varies directly as the square root of y and M is 12 when y is 16.
17) T varies inversely as Q and when Q is 5, T is 10.
18) Z varies inversely as X and when X is 20, Z is 4.
19) N varies jointly as x and y. When x is 2 and y is 3, N is 42.
20) N varies jointly as y and the square of x. When x is 3 and y is 2, N is 54.
Section 2.4 Variation
#21 - 34 Solve.
21) Y varies directly as the cube of x. Y is 24 when x = 2. Find Y when x = 5.
22) Z varies directly as the square of x. Z is 54 when x is 3. Find Z when x = -2
23) W varies inversely as q. W is 10 when q is 5. Find W when q is 3.
24) M varies inversely as the square root of n. M is 15 when n is 9. Find M when n is 16.
25) Y varies jointly as x and the square of z. Y is 48 when z is 2 and x is 3. Find Y when x is 3
and z is 4.
26) B varies jointly as (a) and the square root of c. B is 60 when a is 5 and c is 9. Find B when a
is 4 and c is 16.
27) Suppose that the demand (D) for candy at a movie theater is inversely related to the price
(p). When the price of candy is $2.75 per bag, the theater sells 156 bags of the candy.
Determine the number of bags of candy that will be sold if the price is raised to $3.00 per bag.
28) Suppose that the demand (D) for candy at a movie theater is inversely related to the price
(p). When the price of candy is $4.00 per bag, the theater sells 150 bags of the candy.
Determine the number of bags of candy that will be sold if the price is raised to $5.00 per bag.
29) A gas law states that the volume (V) of an enclosed gas varies directly as the temperature
(T) and inversely as the pressure (P). The pressure of a gas is 0.75 kilogram per square
centimeter when the temperature is 294K and the volume is 8000 cubic centimeters. (round k
to 2 decimal places) Find the volume when the pressure is 1.5 kilogram per square centimeter
and the temperature is 300K.
30) A gas law states that the volume (V) of an enclosed gas varies directly as the temperature
(T) and inversely as the pressure (P). The pressure of a gas is 0.75 kilogram per square
centimeter when the temperature is 294K and the volume is 8000 cubic centimeters (round k to
2 decimal places). Find the volume when the pressure is 2 kilogram per square centimeter and
the temperature is 400K.
31) The distance (D) a ball rolls down an inclined plane is directly proportional to the square of
the time (t) it rolls. In 1 second the ball rolls 8 feet. How far will the ball roll in 3 seconds?
32) The distance (D) a ball rolls down an inclined plane is directly proportional to the square of
the time (t) it rolls. In 1 second the ball rolls 8 feet. How far will the ball roll in 6 seconds?
Section 2.4 Variation
33) The diameter (D) of the largest particle that can be moved by a stream varies directly as the
square of the velocity (V) of the stream. A stream with a velocity of ¼ mile per hour can move
coarse sand particles about 0.02 inch in diameter. How large of a particle can a stream move
that has a velocity of 2 mph?
34) The diameter (D) of the largest particle that can be moved by a stream varies directly as the
square of the velocity (V) of the stream. A stream with a velocity of ¼ mile per hour can move
coarse sand particles about 0.02 inch in diameter. How large of a particle can a stream move
that has a velocity of 5 mph?
Chapter 2 Review
#1-6: Find the x and y-intercepts.
1) 4x - 6y = 12
2) y2 = x + 49
3) y = 2x2 + 13x – 7
5) 𝑦 =
𝑥 2 −5𝑥−6
𝑥+1
𝑥−3
4) 𝑦 = 3𝑥+6
6) x2 + y2 = 121
#7-9. Determine whether the graph is symmetric to the x-axis, y-axis, the origin, or none of
these.
7)
8)
9)
Chapter 2 review
#10 – 12: determine the type of symmetry the graph of the equation has (if any). Make sure to
perform the appropriate test to confirm your answer.
10) y2 = x + 3
11) x2 + y = 6
12) y = x3
#13 – 15: Find the x and y-intercepts then sketch a graph (it will be enough to label two points
on your graph)
13) 2x + 3y = 12
14)
1
2
2
𝑥− 𝑦=5
15)
3
2
3
𝑥 + 2𝑦 = −4
#16 – 19, find an equation for the line with the given properties. Express your answer in slope
intercept form.
16) Slope = 3; containing the point (5, 1)
2
17) Slope = 3; containing the point (-6,2)
18) Parallel to the line y = 2x + 6; containing the point (2,1)
4
19) Parallel to the line 𝑦 = 9 𝑥 − 1; containing the point (3,-1)
#20-21: Write the standard form of the equation of the circle with the given radius (r) and
center (h,k) then sketch a graph of the circle.
20) r = 3 (h,k) = (-3, -1)
21) r = 2 (h,k) = (-5, 4)
#22-23: rewrite so that the equation is written in the standard form of a circle and sketch a
graph.
22) x2 + y2 -6x -4y + 9 = 0
23) x2 + y2 +2x + 4y = 11
#24 - 25: Find the standard form of the equation of each circle. It may help to sketch a graph of
the circle before you start your algebra.
24) Center (-2, 3) contains the point (2, 6)
25) Has a diameter with endpoints (1,4) and (-3,2)
Chapter 2 review
26) M varies inversely as the square root of n. M is 3 when n is 16. Find M when n is 25.
27) Y varies jointly as x and the square of z. Y is 128 when z is 4 and x is 2. Find Y when x is 3
and z is 5.
28) Suppose that the demand (D) for candy at a movie theater is inversely related to the price
(p). When the price of candy is $2.50 per bag, the theater sells 150 bags of the candy.
Determine the number of bags of candy that will be sold it the price is raised to $4.00 per bag,
round your answer to the nearest number of bags.
29) The distance (D) a ball rolls down an inclined plane is directly proportional to the square of
the time (t) it rolls. In 1 second the ball rolls 10 feet. How far will the ball roll in 5 seconds?
Grima MAT 151
Chapter 2 Practice test
#1-2; find an equation for the line with the given properties. Express your answer in slope
intercept form.
1) Slope = -2; containing the point (2, -3)
1
2) Parallel to the line y = 3x - 2; containing the point (6,-5)
3) Write the standard form of the equation of the circle with the given radius (r) and center
(h,k) then sketch a graph of the circle. r = 5 (h,k) = (2, -1)
4) Find the standard form of the equation of each circle. It may help to sketch a graph of the
circle before you start your algebra.
Center (3, 1) contains the point (5, 1)
5) Rewrite so that the equation is written in the standard form of a circle and sketch a graph.
x2 + y2 +6x + 8y = 11
6) Find the x and y-intercepts. x2 + y = 9
7) 𝑦 =
𝑥 2 +11𝑥+10
𝑥−2
8) Find the x and y-intercepts then sketch a graph (it will be enough to label two points on
your graph)
3
5
𝑥 − 2 𝑦 = 15
2
#9-10; determine the type of symmetry the graph of the equation has (if any) Make sure to
perform the appropriate test to confirm your answer. (You need to show the work to get any
credit. 0 points for correct answer without work.)
9) x2 = y - 4
10) y2 = 5x + 1
11) M varies inversely as the square root of n. M is 4 when n is 25. Find M when n is 16.
12) Y varies jointly as the cube of x and the square of z. Y is 144 when x is 2 and z is 3. Find Y
when x is 3 and z is 2.
13) Be able to solve the candy in a theater word problem.
This is problem 28 from section 2.4 and you should be able to solve it too as there will likely be
a problem like this on the test. 28) Suppose that the demand (D) for candy at a movie theater
is inversely related to the price (p). When the price of candy is $4.00 per bag, the theater sells
150 bags of the candy. Determine the number of bags of candy that will be sold if the price is
raised to $5.00 per bag.
14) The distance (D) it takes a car to stop is directly proportional to the square of the speed (s)
it is moving. A car traveling 10 miles per hour can stop in 15 feet. How long will it take a car
traveling 40 miles per hour to stop?
#15 – 17: Determine whether the graph is symmetric to the x-axis, y-axis, the origin, or none of
these.
15)
16)
17)
Answers (I didn’t have room to squeeze the graphs in. Show me your graphs to make sure they
are okay.)
1) y = -2x + 1
1
2) 𝑦 = 3 𝑥 − 7
3) (x-2)2 + (y+1)2 = 25 (graph circle with center (2,-1) with radius of 5)
4) (x-3)2 + (y-1)2 = 4
5) (x+3)2 + (y+4)2 = 36 (graph circle with center (-3,-4) and radius of 6)
6) x-intercepts (-3,0) (3,0) y-intercept (0,9)
7) x-intercepts (-1,0) (-10,0) y-intercept (0,-5)
8) x int (10,0) y-int (0,-6) just plot two points and connect with a line for the graph
9) symmetric to y-axis
10) symmetric to x-axis
11) m = 5
12) y = 216
13) there is no question 13
14) 240 ft
15) symmetric to origin 16) symmetric to x-axis 17) symmetric toy-axis
Grima MAT 151 Chapter 2 in class practice problems
#1-2 Find the x and y-intercepts.
𝑥−4
2) 𝑦 = 3𝑥+2
1) y + 9 = x2
3) Find the x and y-intercepts then sketch a graph (it will be enough to label two points on
3
your graph) 8𝑥 − 4 𝑦 = 24
4) Write the standard form of the equation of the circle with the given radius (r) and center
(h,k) then sketch a graph of the circle. r = 5 (h,k) = (-2, 3)
5) Find the standard form of the equation of each circle. It may help to sketch a graph of the
circle before you start your algebra. Center (2, 5) contains the point (4, 5)
#6-7; find an equation for the line with the given properties. Express your answer in slope
intercept form.
6) Slope = -5; containing the point (2, -3)
7) Parallel to the line y = 2x + 7; containing the point (-5,4)
8) Rewrite so that the equation is written in the standard form of a circle and sketch a graph.
x2 + y2 +10x + 4y = -13
#9-10; determine the type of symmetry the graph of the equation has (if any)
Problems 9 and 10 have been deleted
#11 – 12 Determine whether the graph is symmetric to the x-axis, y-axis, the origin, or none of
these. (5 points each)
11)
12)
13) M varies directly as the square root of n. M is 15 when n is 9. Find M when n is 16.
14) Y varies jointly as the square of x and the cube of z. Y is 256 when x is 4 and z is 2. Find Y
when x is 1 and z is 3.
15) The distance (D) a ball rolls down an inclined plane is directly proportional to the square of
the time (t) it rolls. In 2 seconds the ball rolls 20 feet. How far will the ball roll in 5 seconds?
16) The distance (D) it takes a car to stop is directly proportional to the square of the speed (s)
it is moving. A car traveling 20 miles per hour can stop in 35 feet. How long will it take a car
traveling 25 miles per hour to stop?
This is problem 27 from section 2.4 and you should be able to solve it too as there will likely be
a problem like this on the test. 27) Suppose that the demand (D) for candy at a movie theater
is inversely related to the price (p). When the price of candy is $2.75 per bag, the theater sells
156 bags of the candy. Determine the number of bags of candy that will be sold if the price is
raised to $3.00 per bag.
Answers: 1) x-intercepts (3,0) (-3,0) y-intercept (0,-9) 2) x-intercept (4,0) y-intercept (0,-2)
3) x-intercept (3,0) y-intercept (0,-32)
4) (x+2)2 + (y-3)2 = 25
5) (x-2)2 + (y – 5)2 = 4
6) y = -5x + 7
7) y = 2x + 14
8) (x+5)2 + (y + 2)2 = 16
9) x-axis
10) origin
11) x-axis
13) m = 20
14) y = 54
15) 125 feet
12) origin
16) (k = 7/80 I used k = .0875 to get my answer) 54.6875 feet (okay to round to 54.69 feet)