b.
Calories burned
Juan’s Workout
61. Perimeter of a Square 62.
120
80
40
63.
55. No; each constant change in time (+1 s) is not
accompanied by a constant change in height.
test prep
2
8
2
4
3
12
3
9
4
16
4
16
not linear
Side Length
Volume
1
1
2
8
3
27
4
64
4-2 Using Intercepts
58. G; Each second, sound will move 331 meters. So
the distance covered is 331 times the number of
seconds.
Check it out!
1a. The y-intercept is 3. The x-intercept is -2.
59. Possible answer: 3x + 2y = 7; it is a linear equation
because it can be written in standard form with
A = 3, B = 2, and C = 7.
A table of values also shows it is a linear function:
x
y
-3
8
-2
6.5
-1
5
0
3.5
1
2
2
0.5
Each constant change in x (+1) is accompanied by
a constant change in y (-1.5).
The graph shows a linear function.
2
x
0
b. -3x + 5y= 30
-3x + 5(0) = 30
-3x + 0= 30
-3x= 30
-3x ​=
​ _
  _
​ 30  ​ 
-3
-3
x= -10
The x-intercept is -10.
c. 4x + 2y= 16
4x + 2(0) = 16
4x + 0= 16
4x= 16
4x
_
  _
​   ​=
​ 16 ​ 
4
4
x= 4
The x-intercept is 4.
-3x + 5y= 30
-3(0) + 5y = 30
0 + 5y= 30
5y= 30
5y _
_
  ​ 30 ​ 
​   ​=
5
5
y= 6
The y-intercept is 6.
4x + 2y= 16
4(0) + 2y = 16
0 + 2y= 16
2y= 16
2y
   _
​ _ ​=
​ 16 ​  
2
2
y= 8
The y-intercept is 8.
a. 2x + 3y = 60
2
​
​ ____ 
-2x​
​-2x
________ 
3y= 60 - 2x
3y _
2x 
​ _ ​=
  ​ 60 - ​
 
3
3
2
_
y= 20 - ​   ​ x
3
x
0
6
2
_
y = 20 - ​    ​ x
20
16
3
y
4
2
Both the graph and the table show solutions to the
equation.
challenge and extend
60. y = 0; x = 0; the first describes a linear function, but
the second does not.
15
24
30
10
4
0
Notebooks
School Store Purchases
20
10
0
1
not linear
57. C; C is not linear, because x appears in the
denominator of a fraction.
Area
1
Volume of a Cube
56. Yes; the equation can be written in standard form
with A = 1, B = 0, and C = 9. No; all solutions
are ordered pairs with x-value 9. The x-value 9
corresponds to more than one y-value.
-2
Side Length
4
linear
10 20
Time (min)
Area of a Square
1
Side Length Perimeter
160
0
c. The graph forms a
line.
109 10
20
Pens
30
The x-intercept is 30. The y-intercept is 20.
Holt McDougal Algebra 1
b. x-intercept: pens that can be purchased if no
notebooks are purchased.
y-intercept: notebooks that can be purchased if no
pens are purchased.
a. x-intercept:
3
-3x + 4y= -12
-3x + 4(0) = -12
-3x= -12
-3x
_
​   ​=
  _
 
​ -12 ​ 
-3
-3
x= 4
y
y-intercept:
-3x + 4y= -12
-3(0) + 4y = -12
4y= -12
4y _
_
   ​ -12
 
​   ​=
 ​ 
4
4
y= -3
2
4
-2
y= _
​ 1 ​ x - 2
3
3(y)= 3​ _
​ 1 ​ x - 2 ​
3
3y= x - 6
-x + 3y = -6
x-intercept:
-x + 3y= -6
-x + 3(0) = -6
-x= -6
-1(-x)= -1(-6)
x= 6
y
b.
(
)
2
y-intercept:
-x + 3y= -6
-(0) + 3y = -6
3y= -6
3y _
_
​   ​=
   ​ -6 ​  
3
3
y= -2
x
0
2
6
-3x - 2y= -6
-3x - 2(0) = -6
-3x - 0= -6
-3x= -6
-3x
_
​   ​=
  _
​ -6 
 ​ 
-3
-3
x= 2
The x-intercept is 2.
-3x - 2y= -6
-3(0) - 2y = -6
0 - 2y= -6
-2y= -6
-2y _
_
  ​ -6 
​   ​=
 ​
-2
-2
y= 3
The y-intercept is 3.
7. 4y + 5x = 2y - 3x + 16
​
​ -2y
  ​
​-2y
________ 
_____________
2y + 5x =
-3x + 16
​_______ 
+ 3x​​________ 
+3x
​
2y + 8x = 16
8x + 2y = 16
8x + 2y= 16
8x + 2y= 16
8x + 2(0) = 16
8(0) + 2y = 16
8x + 0= 16
0 + 2y= 16
8x= 16
2y= 16
8x
16
2y
_
_
_
​   ​=
  ​   ​ 
  _
​   ​=
​ 16 ​  
8
8
2
2
x= 2
y= 8
The x-intercept is 2.
The y-intercept is 8.
8a. x
-4
2x - 4y= 4
2(0) - 4y = 4
0 - 4y= 4
-4y= 4
-4y _
_
​   ​=
  ​  4  ​ 
-4
-4
y= -1
The y-intercept is -1.
6.
-2y= 3x - 6
-3x​​_______ 
-3x
​
​____ 
-3x - 2y = -6
x
0
5. 2x - 4y= 4
2x - 4(0) = 4
2x - 0= 4
2x= 4
2x
_
  _
​ 4 ​ 
​   ​=
2
2
x= 2
The x-intercept is 2.
0
1
2
3
4
f(x) = -25 + 5x -25 -20 -15 -10 -5
think and discuss
1. (4, 0) and (0, 2)
0
Refrigeration Tank Temperature
Time (h)
2. 4.318; -21.5489
0
3.
Temperature (°C)
2. Find the y-intercept
by letting x equal
0 and solving for y.
2
4
6
-5
Graphing Ax + By = C
Using Intercepts
1. Find the x-intercept
by letting y equal
0 and solving for x.
5
3. Graph the line by
plotting the points
containing the intercepts
and then connecting the
points with a straight line.
1. y-intercept
-15
-20
-25
The x-intercept is 5. The y-intercept is -25.
EXERCISES
guided practice
-10
b. x-intercept: time when temperature is 0°C
y-intercept: initial temperature
2. The x-intercept is -5. The y-intercept is 1.
3. The x-intercept is 2. The y-intercept is -4.
4. The x-intercept is -3. The y-intercept is -2.
110 Holt McDougal Algebra 1
9. x-intercept:
4x - 5y= 20
4x - 5(0) = 20
4x= 20
4x
_
​   ​=
  _
​ 20 ​ 
4
4
x= 5
y
0
y-intercept:
4x - 5y= 20
4(0) - 5y = 20
-5y= 20
-5y _
_
  ​ 20  ​ 
​   ​=
-5
-5
y= -4
x
2
-2
-4
0.
1
y = 2x + 4
-2x + y = 4
x-intercept:
-2x + y = 4
-2x + 0 = 4
-2x= 4
-2x ​=
​ _
 
  _
​  4  ​ 
-2
-2
x= -2
y-intercept:
-2x + y= 4
-2(0) + y = 4
y= 4
y
4
x
0
-4
2
11. x-intercept:
1 ​ x - _
​ 1 ​ y= 2
​ _
3
4
1  ​x  - _
​ _
​ 1 ​ (0) = 2
3
4
1 ​ x= 2
​ _
3
3​ _
​ 1 ​ x ​= 3(2)
3
x= 6
( )
y
-4
0
y-intercept:
1  ​x  - _
​ 1 ​ y= 2
​ _
3
4
1  ​(  0) - _
​ _
​ 1 ​ y = 2
3
4
1 ​ y= 2
-​ _
4
1
_
-4​ -​   ​ y ​= -4(2)
4
y= -8
( )
x
4
-4
-8
2. x-intercept:
1
-5y + 2x= -10
-5(0) + 2x = -10
2x= -10
2x
_
​   ​=
   _
 
​ -10
 ​ 
2
2
x= -5
y
y-intercept:
-5y + 2x= -10
-5y + 2(0) = -10
-5y= -10
-5y _
_
  ​ -10 ​ 
 
​   ​=
-5
-5
y= 2
practice and problem solving
13. The x-intercept is -1. The y-intercept is 3.
14. The x-intercept is -5. The y-intercept is -1.
15. The x-intercept is -4. The y-intercept is 2.
6. 6x + 3y= 12
1
6x + 3(0) = 12
6x + 0= 12
6x= 12
6x
_
​   ​=
  _
​ 12 ​ 
6
6
x= 2
The x-intercept is 2.
7.
1
4y - 8= 2x
-2x​ -2x
​______ 
4y - 2x - 8 = 0
​__________
+
  
8​​+8​
___ 
4y - 2x
= 8
-2x + 4y= 8
-2x + 4y= 8
-2x + 4(0) = 8
-2x + 0= 8
-2x= 8
-2x
_
​   ​=
  _
​  8  ​ 
-2
-2
x= -4
The x-intercept is -4.
8. -2y + x =2y - 8
1
​
​ _______ 
-2y
​
​-2y
_______ 
-4y + x = -8
x - 4y= -8
x - 4y= -8
x - 4(0) = -8
x - 0= -8
x= -8
The x-intercept is -8.
6x + 3y= 12
6(0) + 3y = 12
0 + 3y= 12
3y= 12
3y _
_
   ​ 12 ​  
​   ​=
3
3
y= 4
The y-intercept is 4.
-2x + 4y= 8
-2(0) + 4y = 8
0 + 4y= 8
4y _
   ​ 8 ​ 
​ _ ​=
4
4
y= 2
The y-intercept is 2.
x - 4y = -8
0 - 4y = -8
-4y= -8
-4y _
​ _ ​=
 
  ​ -8 ​ 
-4
-4
y= 2
The y-intercept is 2.
9. 4x + y = 8
1
4x + 0 = 8
4x= 8
4x ​=
  _
​ 8 ​ 
​ _
4
4
x= 2
The x-intercept is 2.
4x + y= 8
4(0) + y = 8
0 + y= 8
y= 8
The y-intercept is 8.
0. y - 3x = -15
2
0 - 3x = -15
-3x= -15
-3x ​=
​ _
  _
​ -15 ​ 
-3
-3
x= 5
The x-intercept is 5.
y - 3x= -15
y - 3(0) = -15
y - 0= -15
y= -15
The y-intercept is -15.
x
-4
-2
0
-2
111 Holt McDougal Algebra 1
1. 2x+ y = 10x - 1
2
​-10x
​
​ ________ 
-10x
​
________ 
-8x+ y = -1
-8x + y = -1
-8x + 0 = -1
-8x= -1
-8x ​=
​ _
 
  _
​ -1 
 ​ 
-8
-8
1 ​  
x= ​ _
8
The x-intercept is _
​ 1 ​ .
8
22a. x
-8x + y= -1
-8(0) + y = -1
0 + y= -1
y= -1
The y-intercept is -1.
3
6
9
12
225
150
75
0
x
0
Population
210
140
( )
4
8
12
Time (yr)
23a. x
1  ​ x
f(x) = 5 - ​ _
5
y
4
0
5
15
20
25
5
4
2
1
0
7. x-intercept:
2
y - x= -1
0 - x= -1
-x= -1
-1(-x) = -1(-1)
x= 1
he x-intercept is 25. The
T
y-intercept is 5.
3
x
8
-4
5K Race
4
y-intercept:
1  ​x  - 4y= 4
​ _
2
1
_
​    ​(  0) - 4y = 4
2
-4y= 4
-4y _
_
  ​  4  ​ 
​   ​=
-4
-4
y= -1
4
The x-intercept is 12. The y-intercept is 300.
Distance to finish line (km)
8
b. x-intercept: time when bass population is 0
y-intercept: number of bass originally in the lake
y-intercept:
y - x = -1
y - 0 = -1
y= -1
y
2
2
1
x
0
-2
10 20
Time (min)
b. x-intercept: total time to run the race (when the
distance to the finish line is 0)
y-intercept: total length of the race (when time is 0)
4. x-intercept:
2
4x - 6y= 12
4x - 6(0) = 12
4x= 12
4x
_
​   ​=
  _
​ 12 ​ 
4
4
x= 3
4
y-intercept:
4x - 6y= 12
4(0) - 6y = 12
-6y= 12
-6y
  _
​ _ ​=
​ 12  ​ 
-6
-6
y= -2
0
0
2
8. x-intercept:
2
5x + 3y= 15
5x + 3(0) = 15
5x= 15
5x
_
​   ​=
  _
​ 15 ​ 
5
5
x= 3
y
y-intercept:
5x + 3y= 15
5(0) + 3y = 15
3y= 15
3y _
_
  ​ 15 ​  
​   ​=
3
3
y= 5
4
y
2
x
2
-2
4
26. x-intercept:
1 ​ x - 4y= 4
​ _
2
1  ​x  - 4(0) = 4
​ _
2
1 ​ x= 4
​ _
2
2​ _
​ 1  ​x  ​= 2(4)
2
x= 8
Bass Population
0
2
70
y-intercept:
2x + 3y= 18
2(0) + 3y = 18
3y= 18
3y _
_
  ​ 18 ​  
​   ​=
3
3
y= 6
y
6
280
4
0
f(x) = 300 - 25x 300
5. x-intercept:
2
2x + 3y= 18
2x + 3(0) = 18
2x= 18
2x
_
​   ​=
  _
​ 18 ​ 
2
2
x= 9
4x
-2
0
2
-2
-4
112 Holt McDougal Algebra 1
9. x-intercept:
2
x - 3y= -1
x - 3(0) = -1
x= -1
y-intercept:
x - 3y = -1
0 - 3y = -1
-3y= -1
-3y _
​ _ ​=
  ​ -1 
 ​
-3
-3
y= _
​ 1 ​ 
3
y
2
x
0
2
b.
-x + y= 4
-(0) + y = 4
0 + y= 4
y= 4
The y-intercept is 4.
b. x-intercept: the number of years after 1800 when
there will be no acres of tropical forest
y-intercept: million acres of tropical forest in 1800
32a. m
0
b = 412 - 4m 412
Account Balance
Balance ($)
380
340
300
20
40
60
80
332
252
172
92
b.
y = 412 - 4x
​
+4x​
_
​ _______ 
+ 4x​
____ 
BUA111FT-BKMADD-A732
4x + y = 412
4x + y = 412
4x + y= 412
4x + 0 = 412
4(0) + y = 412
4x= 412
0 + y= 412
4x ​=
y= 412
​ _
  _
 
​ 412
 ​ 
4
4
x= 103
The y-intercept is 412.
The x-intercept is 103. x-intercept: number of months from that time until
the account has $0
y-intercept: balance when bank employee noticed
the account
x=1
x=5
y
x
4
-8
y = -3
4
8
-2x - y= 4
-2(0) - y = 4
0 - y= 4
-y= 4
-1(-y)= -1(4)
y= -4
The y-intercept is -4.
Graph D has an x-intercept of -2 and a y-intercept
of -4.
7. 4x - 2y= 8
3
4x - 2y= 8
4x - 2(0) = 8
4(0) - 2y = 8
4x - 0= 8
0 - 2y= 8
4x= 8
-2y= 8
4x ​=
-2y _
_
​ _
  _
​ 8 ​ 
​   ​=
 
  ​  8  ​ 
4
4
-2
-2
x= 2
y= -4
The x-intercept is 2.
The y-intercept is -4.
Graph B has an x-intercept of 2 and a y-intercept
of -4.
c. After 103 months or 8 years and 7 months.
-4
8
6. 2y + 4x= 8
3
2y + 4x= 8
2(0) + 4x = 8
2y + 4(0) = 8
0 + 4x= 8
2y + 0= 8
4x= 8
2y= 8
8
4x
2y
_
_
8 ​ 
_
​   ​=
  ​   ​ 
​   ​=
   ​ _
4
4
2
2
x= 2
y= 4
The x-intercept is 2.
The y-intercept is 4.
Graph A has an x-intercept of 2 and a y-intercept of 4.
2
4
6
Time (mo)
0
4
5.
3
y = 4 - 2x
​____ 
+2x​​______ 
+ 2x​
2x + y = 4
2x + y= 4
2x + y= 4
2x + 0 = 4
2(0) + y = 4
2x= 4
0 + y= 4
2x
4
_
_
y= 4
​   ​=
  ​   ​ 
2
2
The y-intercept is 4.
x= 2
The x-intercept is 2.
Graph A has an x-intercept of 2 and a y-intercept
of 4.
he number of months
T
must be a whole number
so the domain is (0, 1,
2, 3, ...}. The range is
{$412, $408, $404,
$400, ...}.
420
-4
0
4.-2x - y= 4
3
-2x - 0 = 4
-2x= 4
-2x
_
​   ​=
  _
​  4  ​ 
-2
-2
x= -2
The x-intercept is -2.
31a. The y-intercept is approximately 7.5. The
x-intercept is approximately 600.
-8
-4
y = -3: no x-intercept,
y-intercept: -3
y = 2: no x-intercept,
y-intercept: 2
y = 7: no x-intercept,
y-intercept: 7
-8
c. The original height of the bamboo plant.
33a. x = -6
y=2
c. Horizontal: For y = c, the y-intercept is c and there
is no x-intercept.
Vertical: For x = k, the x-intercept is k, and there is
no y-intercept.
b.
y = x + 4
  -x
​
​-x​
___​
______ 
-x + y = 4
0
4
-4
30a. y = x + 4
y=7
x
-8
-2
y
x = -6: x-intercept: -6,
no y-intercept
x = 1: x-intercept: 1,
no y-intercept
x = 5: x-intercept: 5,
no y-intercept
38a. The x-intercept is 20. The y-intercept is 1.75.
b. x-intercept: time remaining when Kristyn started
her workout
y-intercept: total distance Kristyn covered
39. Possible answer: Jen wants to save $60. Each week
she will earn $12. The function shows how much
money Jen has left to save each week.
113 Holt McDougal Algebra 1
test prep
3 ​ x + 6
y =​ _
8
3
3
​​-​ _ ​ x
 
​
​-​ _ ​ x 
8
8
____
________
45.
40. D; Notice that -2(9) = -18 = 0 - 18 = 9(0) - 18.
So, (9, 0) is on -2x = 9y - 18 and therefore is the
x-intercept.
41. F; The y-intercept is -200 so Jamie owed her uncle
$200. The x-intercept is 40 so Jamie was paying her
uncle for 40 weeks.
2. 60x + 55y= 660
4
60(0) + 55y = 660
0 + 55y= 660
55y= 660
55y _
_
​   ​=
 
  ​ 660 ​ 
55
55
y= 12
The y-intercept is 12.
3
6
-​ _  ​x  + y = 8
x-intercept:
3
-​ _ ​ x + y= 6
8
3
-​ _  ​x  + 0= 6
8
3
-​ _ ​ x= 6
8
8 3
8
-​ _  ​​  -​ _ ​ x ​= -​ _ ​ (6)
3 8
3
x= -16
y-intercept:
3
-​ _ ​ x + y= 6
8
3
-​ _  ​(  0) + y = 6
8
y= 6
( )
y
challenge and extend
43. x-intercept:
1 ​ x + _
​ 1 ​ y= 1
​ _
2
5
1  ​x  + _
​ _
​ 1 ​ (0) = 1
2
5
1 ​ x= 1
​ _
2
2​ _
​ 1 ​ x ​= 2(1)
2
x= 2
( )
y-intercept:
1  ​x  + _
​ 1 ​ y= 1
​ _
2
5
1  ​(  0) + _
​ _
​ 1 ​ y = 1
2
5
1 ​ y  = 1
​ _
5
5​ _
​ 1 ​ y ​= 5(1)
5
y= 5
( )
y
4
2
x
-2
0
2
4. x-intercept:
4
0.5x - 0.2y= 0.75
0.5x - 0.2(0) = 0.75
0.5x= 0.75
0.5x
_
​   ​=
  _
​ 0.75 ​ 
0.5
0.5
x= 1.5
y
-2
0
x
2
y-intercept:
0.5x - 0.2y= 0.75
0.5(0) - 0.2y = 0.75
-0.2y= 0.75
-0.2y _
_
  ​ 0.75 
​ 
 ​=
 ​ 
-0.2
-0.2
y= -3.75
x
-12 -6
0
-6
6. Ax + By= C
4
Ax + B(0) = C
Ax + 0= C
Ax= C
Ax ​ = _
​ _
​ C ​ 
A
A
x= _
​ C ​ 
A
The x-intercept is _
​ C ​  .
A
Ax + By= C
A(0) +By = C
0 + By= C
By= C
By _
_
​   ​ = ​ C ​ 
B
B
C
_
y= ​   ​ 
B
The y-intercept is _
​ C ​ .
B
7. 22x - 380y= 20,900 22x - 380y= 20,900
4
22x - 380(0) = 20,900 22(0) - 380y = 20,900
22x - 0= 20,900 0 - 380y= 20,900
22x= 20,900 -380y= 20,900
20,900
-380y _
20,900
22x
_
_
_
  ​ 
 
​   ​=
 ​ 
  ​ 
 
​ 
 ​=
 ​ 
22
22
-380
-280
x= 950
y= -55
The x-intercept is 950. The y-interecpt is -55.
Possible answer: scale on the x-axis should include
numbers from 0 to a number a little greater than
950; scale on y-axis should include numbers from a
little less than -55 to 0.
-2
-4
114 Holt McDougal Algebra 1