Download Chapter 10: Writing and solving systems of linear functions

Chapter 10: Writing and solving systems of linear functions
EQUATION OF A LINE AND PARALLEL LINES
1.What is the slope of the graph of the equation y = 2x -
1.
2.
2
3.
4.
2x
?
2.The line whose equation is y = 4x + 2 has a y-intercept whose coordinates are
1.
2.
3.
4.
(0, 0)
(0, 2)
(4, 0)
(0, 4)
3.What is the slope of the line whose equation is y = 3x 5?
1.
2.
3.
4.
-5
5
3
3x
4.What is the slope of the line with the equation y =
x + 4?
1.
2.
3.
4.
x
4
4x
5.An equation whose graph has a slope of 2 and a y-intercept of 3 is
1.
2.
3.
4.
x = -2 y + 3
y = -2x + 3
x=3y 2
y = 3x 2
1
6.What is the y-intercept of the graph of the equation y = -
1.
2.
3.
4.
x + 4?
-2
3
4
7.Which equation represents the line whose slope is
1. y =
and whose y-intercept is 5?
x+5
2. y = 5x +
3. y =
x-5
4. y = 5x 8.Write an equation of the line whose slope is 2 and whose y-intercept is -3.
1.
2.
3.
4.
y = -3x + 2
y = 2x 3
2y = -3x
-3y = 2x
9.What is the slope of the line whose equation is 3x 4y 16 = 0?
1.
2.
3. 3
4. -4
2
10.The accompanying graph represents the yearly cost of playing 0 to 5 games of golf at the Shadybrook
Golf Course. The total cost of joining the club and playing 10 games during the year is $
11.If a straight line with slope 5 contains the points (1, 2) and (3, K), the value of K is
.
.
12.Connor wants to compare Celsius and Fahrenheit temperatures by drawing a conversion graph. He
knows that -40°C = -40°F and that 20°C = 68°F. Use a grid to construct the conversion graph and
determine the Celsius equivalent of 25°F. Round your answer to the nearest integer.
25°F =
°C
13.What is the slope of the line whose equation is 2y = 5x+ 4?
1. 5
2. 2
3.
4.
14.If x and y are defined as indicated by the accompanying table, which equation correctly represents the
relationship between x and y?
1. y = x + 2
3
2. y = 2x + 2
3. y = 2x + 3
4. y = 2x - 3
15.Which linear equation represents the data in the accompanying table?
1.
2.
3.
4.
d = 1.50c
d = 1.50c + 20.00
d = 20.00c + 1.50
d = 21.50c
16.Which graph represents the equation x = 2?
17.What is the y-intercept of the graph of the line whose equation is
?
1. 2. 3. 0
4. 4
18.Which statement describes the graph of x = 4?
1. It passes through the point (0,4).
2. It has a slope of 4.
4
3. It is parallel to the y-axis.
4. It is parallel to the x-axis.
19.The graph of the equation x + 3y = 6 intersects the y-axis at the point whose coordinates are
1.
2.
3.
4.
(0,2)
(0,6)
(0,18)
(6,0)
20.Which phrase describes the graph of y = -1 on the coordinate plane?
1.
2.
3.
4.
a line parallel to the y-axis and 1 unit to the right of it
a line parallel to the y-axis and 1 unit to the left of it
a line parallel to the x-axis and 1 unit below it
a line parallel to the x-axis and 1 unit above it
21.Which equation represents the line parallel to the y-axis and 4 units to the left of the y-axis?
1.
2.
3.
4.
x=4
x = -4
y = -4
y=4
22.Which statement is true about the graph of the line whose equation is y = 8?
1.
2.
3.
4.
The line is parallel to the x-axis.
The line is parallel to the y-axis.
The line passes through the origin.
The line has a slope of 8.
23.Which equation is represented by the graph of line L?
1. x = y + 4
2. y = x + 4
3. x = 4
5
4. y = 4
25.The accompanying figure shows the graph of the equation x = 5. What is the slope of the line x = 5?
1.
2.
3.
4.
5
-5
0
undefined
26.What is the equation of the line containing the points (6, 3), (6, 8) and (6, -13)?
1.
2.
3.
4.
x=6
y=6
y = 2x – 6
y = -13
27.What is the equation of the line containing the points (-2, 1), (-2, 8) and (-2, -1)?
1.
2.
3.
4.
x=2
y = -2
x = -2
y=8
28.What is the equation of the line containing the points (2, -1), (5, -1) and (-7, -1)?
1.
2.
3.
4.
x=2
y = -1
x = -7
y=x-1
29.What is the equation of the line containing the points (10, 5), (-6, 5) and (13, 5)?
1. y = 5
2. y = -1
6
3. x = 10
4. y = 5x - 10
28.What is the equation of the locus of points 4 units to the right of the y-axis?
1.
2.
3.
4.
x=4
y = -4
y = 4x – 10
x = -4
29.Which properties best describe the coordinate graph of two distinct parallel lines?
1.
2.
3.
4.
same slopes and same intercepts
same slopes and different intercepts
different slopes and same intercepts
different slopes and different intercepts
30.Shanaya graphed the line represented by the equation y = x - 6. An equation for a line that is parallel
to the given line is
1.
2.
3.
4.
y = 2x - 6
2y = x - 6
y=x+6
y = -x - 6
31.Shanaya graphed the line represented by the equation y = x - 6. An equation for a line that is identical
to the given line but has different coefficients is
1.
2.
3.
4.
2y = 2x - 12
2y = x - 6
y=x+6
y = -x - 6
32.Which equation represents a line that is parallel to the line whose equation is 2x + 3y = 12?
1.
2.
3.
4.
6y - 4x = 2
6y + 4x = 2
4x - 6y = 2
6x + 4y = -2
33.When solved graphically, which system of equations will have exactly one point of intersection?
1. y = -x - 20, y = x + 17
2. y = 0.5x + 30, y = 0.5x - 30
3. y =
x + 12, y = 0.6x - 19
7
4. y = -x + 15, y = -x + 25
34.Write an equation of a line parallel to the line
and having the y-intercept of (0, -2).
1.
2.
3.
4.
35.Write an equation of a line parallel to the line
and passing through the point (0, 1).
1.
2.
3. y = 2x + 1
4. y = 2x + 1
36.The equation of a given line is 3y - 2 = 6x + 4. Which could be the equation of a line parallel to the
given line that passes through the point (1, -5)?
1.
2.
3.
4.
y= x-3
y + 5 = 2(x + 1)
y = 2x - 7
y = 2x + 7
37.The equation of a given line is 3x + 12 = x + 4y. A line parallel to the given line passes through the
point (-4, -3). Which could be the equation of this line?
1. y = x + 1
2. y + 4 = 4(x + 3)
3. y = 4x + 8
4. y =
x-1
8
38.Which of the following equations is parallel to the line that passes through the points (2, 1) and (6, 1)?
1. y =
x-2
2. y - 1 = -
(x - 2)
3. y + 1 = -
(x + 6)
4. y = -
x-1
39.Which is the equation of a line not parallel to y = -4x - 6?
1.
2.
3.
4.
4y + 6 = -16x - 10
2y = 8x + 12
14 - y = 4x + 12
2x + 3y - 4 = -10x + 5
40.Which of the following equations represents a line that is not parallel to the line 2x + 5 - 4y = 2y - 4
+8x?
1.
2.
3.
4.
-y = x - 5
2y = -2x - 12
x = -y - 8
1 - 4y = -4x - 172
Systems of Equations and Inequalities
1.Solve the following system of equations graphically and check:


x=
3y = - 2x + 12
y x=4
and y =
2.Solve the following system of equations graphically and check:
x=

y-x=1

y=-
x+4
and y =
.
9
3.
Two video rental clubs offer two different rental fee plans: Club A charges $12 for
membership and $2 for each rented video. Club B has a $3 membership fee and charges
$3 for each rented video. The graph represents the total cost of renting videos from Club
A.
(a) An equation of the line representing the total cost of renting videos from Club B is y
=
x+
.
(b) For what number of video rentals is it less expensive to belong to Club A?
videos
4.At which point will the graphs of the equations 2x + y = 8 and x y = 4 intersect?
1.
2.
3.
4.
(0, 4)
(4, 0)
(-4, 0)
(5, -2)
10
5.The diagram represents the graphs of the inequalities y 3 and x -2. Which ordered
pair names a point in the solution set of this system of inequalities?
1.
2.
3.
4.
(3, 5)
(3, -5)
(-3, 5)
(-3, -5)
6.Solve the following system of equations graphically and check:


x=
y+x=4
3y - x = -12
, and y =
7.Solve the following system of equations graphically, and check:


x=
.
x + 2y = 4
y = 2x + 7
, and y =
.
11
8.Two health clubs offer different membership plans. The accompanying graph
represents the total cost of belonging to Club A and Club B for one year.
(a) If the yearly cost includes a membership fee plus a monthly charge, the membership
fee for Club A is $
.
(b) The number of the month when the total cost is the same for both clubs is
(c) The total cost for Club A when both plans are the same is $
(d) The monthly charge for Club B is $
.
.
.
9.The Excel Cable Company has a monthly fee of $32.00 and an additional charge of
$8.00 for each premium channel. The Best Cable Company has a monthly fee of $26.00
and an additional charge of $10.00 for each premium channel. The Horton family is
deciding which of these two cable companies to subscribe to.
(a) For what number of premium channels will the total monthly subscription fee for the
Excel and Best Cable companies be the same?
channels
(b) The Horton family decides to subscribe to 2 premium channels for a period of one
year. Which cable company should they subscribe to in order to spend less money,
Excel or Best?
(c) How much money will the Hortons save in one year by using the less expensive
company? $
11.Which point is in the solution set of the system of inequalities shown in the
accompanying graph?
12
1.
2.
3.
4.
(0,4)
(2,4)
(-4,1)
(4,-1)
12.Which coordinate point is in the solution set for the system of inequalities shown in
the accompanying graph?
1.
2.
3.
4.
(3,1)
(2,2)
(1,-1)
(0,1)
13.Which ordered pair is in the solution set of the system of inequalities shown in the
accompanying graph?
13
1.
2.
3.
4.
(0,0)
(0,1)
(1,5)
(3,2)
14.Solve the following system of equations for x:


1.
2.
3.
4.
4x + y = 11
x+y=2
-1
2
3
27
15.Solve the following system of equations algebraically:


2y = 8  x
y  2x = 1
The solution is x =
,y=
16.Solve the following system of equations for x:


1.
2.
3.
4.
2x + y = 4
x 2y=7
2
3
5
7
14
17.Solve the following system of equations algebraically and check:


2x + 3y = 11
5x 2y = 20
The solution is: x =
,y=
.
18.Which ordered pair is the solution set for this system of equations?


1.
2.
3.
4.
x+y=8
y=x 3
(2.5, 2.5)
(4, 1)
(4, 4)
(5.5, 2.5)
19.Solve the following system of equations algebraically and check:


x=
2x = 5 y + 8
3x + 2 y = 31
and y =
20.Solve the following system of equations for y:


2x + y = 12
2x + 3 y = 4
1.
2.
3.
4.
8
2
3
4
21.Solve the following system of equations algebraically or graphically, and check:


x=
3y = 2x 6
x+y=8
,y=
22.What is the solution for the following system of equations?


1.
x=-y
x+2y=6
(-2, 2)
15
2.
3.
4.
(2, -2)
(6, -6)
(-6, 6)
23.Solve the following system of equations algebraically and check:


x=
3x + y = 3
y = 2x 7
,y=
24.Solve for x:


1.
2.
3.
4.
2x - y = 3
x+y=3
1
2
-1
6
25.Solve the following system of equations algebraically and check:


x=
3x - 5y = -6
2x - 3y = -5
, and y =
26.Solve the following system of equations for x:


1.
2.
3.
4.
5x + y = 19
2x + y = 1
-11
6
3
18
27.Solve the following system of equations algebraically, and check:


x=
x+2y=4
y = 2x + 7
, and y =
28.Solve the following system of equations for x:

2x + y = 6
16

1.
2.
3.
4.
3x y = 4
-1
2
10
4
29.Solve the following system of equations algebraically and check:


4x - 5y = 18
3x - 2y = 10
x=
and y =
.
30.Which ordered pair is the solution to this system of equations?


y=x+4
x+y=2
1.
2.
3.
4.
(1, 5)
(0, 2)
(-1, 3)
(-4, 0)
31.Solve the following system of equations algebraically and check:


y = 2x
x+y=6
x=
and y =
32.Solve the following system of equations algebraically and check:


2x + 3y = 17
3x - 2y = -0.5
x=
, and y =
.
33.The sophomore class at South High School raised $800 from the sale of tickets to a
dance. Tickets sold for $1.50 in advance, and $2.00 at the door. If a total of 475 tickets
were sold, the number of tickets sold at the door was
.
34Solve the following system of equations for x:


1.
2x + y = 10
3x = y
6
17
2.
3.
4.
2
-4
4
35.Solve the following system of equations for y:


1.
2.
3.
4.
2x + y = 10
3x = y
6
2
-4
4
36.What is a solution for the system of equations x y = 2 and y = 2x 4?
1.
2.
3.
4.
(0, 2)
(2, 0)
(3, 2)
(4, 2)
37.What is the value of y in the following system of equations?
2x + 3y = 6
2x + y = -2
1.
2.
3.
4.
1
2
-3
4
38.Which ordered pair is the solution of the following system of equations?
3x + 2y = 4
-2x + 2y = 24
1.
2.
3.
4.
(2, -1)
(2, -5)
(-4, 8)
(-4, -8)
39.Tanisha and Rachel had lunch at the mall. Tanisha ordered three slices of pizza and
two colas. Rachel ordered two slices of pizza and three colas. Tanisha's bill was $6.00,
and Rachel's bill was $5.25.
18
What was the price of one slice of pizza? $
What was the price of one cola? $
40.Alexandra purchases two doughnuts and three cookies at a doughnut shop and is
charged $3.30. Briana purchases five doughnuts and two cookies at the same shop for
$4.95. All the doughnuts have the same price and all the cookies have the same price.
Find the cost of one doughnut and the cost of one cookie.
The cost of one doughnut is $
The cost of one cookie is $
.
.
42.What point is the intersection of the graphs of the lines 2x - y = 3 and x + y = 3?
1.
2.
3.
4.
(2,1)
(1,2)
(3,0)
(3,3)
43.At the local video rental store, José rents two movies and three games for a total of
$15.50. At the same time, Meg rents three movies and one game for a total of $12.05.
How much money is needed to rent a combination of one game and one movie?
Answer: $
44.Sharu has $2.35 in nickels and dimes. If he has a total of thirty-two coins, how many
of each coin does he have?
Nickels =
Dimes =
19