Intermediate Algebra
Graphing Linear Equations Using x- and y-Intercepts
Name _____________________________
y
1. Graph x  y  3 using x- and y-intercepts.
x-int: (
if y=0,
, 0)
y-int: (0 ,
if x=0,
)
x
y
2. Graph x  2 y  6 using x- and y-intercepts.
x-int: (
if y=0,
, 0)
y-int: (0 ,
if x=0,
)
x
3. Graph 2 x  5 y  10 using x- and y-intercepts.
x-int: (
if y=0,
, 0)
y-int: (0 ,
if x=0,
y
)
x
4. Graph  x  2 y  1 using x- and y-intercepts.
x-int: (
if y=0,
, 0)
y-int: (0 ,
if x=0,
y
)
x
y
Answers:
1. Graph x  y  3
(0, 3)
x-int: (3, 0)
if y=0,
x0  3
x3
y-int: (0, 3)
if x=0,
0 y  3
(3, 0)
x
y3
y
2. Graph x  2 y  6
x-int: (6, 0)
if y=0,
x  2(0)  6
x6
y-int: (0, -3)
if x=0,
0  2y  6
y  3
(6, 0)
x
(0, -3)
y
3. Graph 2 x  5 y  10
x-int: (5, 0)
if y=0,
2 x  5(0)  10
x5
y-int: (0 , 2)
if x=0,
2(0)  5 y  10
(0, 2)
(5, 0)
x
y2
y
4. Graph  x  2 y  1
x-int: (-1, 0)
if y=0,
 x  2(0)  1
x  1
y-int: (0, ½)
if x=0,
 0  2y  1
y
1
2
(0, ½ )
(-1, 0)
x
Solutions to Linear Equations in Two Variables
1. Complete the following x-y table for:
2x  3 y  6
x
y
0
2. Complete the following x-y table for:
4 x  2 y  6
x
y
0
0
-9
1 
3. Determine if  ,3  is a solution to the
3 
equation 3x  y  4 .
0
-8
1

4. Determine if  ,3  is a solution to the
3

equation 3x  y  4 .
5. Say the weekly profit, P(n), of a video rental store can be approximated by the formula
P(n)  1.5n  200 , where n is the number of videos rented weekly.
a. If the store rented 500 videos would it make a weekly profit of $550?
b. If the store rented 600 videos would it make a weekly profit of $650?
c. If the store rented 300 videos, how much weekly profit would the store make?
d. If the store made a weekly profit of $775, how many videos did the store rent?
6. Say the weekly profit, P(n), of a widget store can be approximated by the formula P(n)  0.07n  300 ,
where n is the number of widgets sold.
a. If the store sold 500 widgets would it make a weekly profit of $335?
b. If the store sold 600 widgets would it make a weekly profit of $350?
c. If the store sold 300 widgets, how much weekly profit would the store make?
d. If the store made a weekly profit of $314, how many widgets did the store sale?
Answers:
1.
(0, 2)
(3, 0)
(-9, 8)
2.
(0, 3)
(-3/2, 0)
(-8, -13)
3.
No, not a solution
4.
Yes, it is a solution
5.
a. Yes, 500 videos makes a weekly profit of $550
b. No, 600 videos does not make a weekly profit of $650
c. 300 videos makes a weekly profit of $250
d. A weekly profit of $775 is from 650 videos
6.
a. Yes, 500 widgets makes a weekly profit of $335
b. No, 600 widgets does not make a weekly profit of $350
c. 300 widgets makes a weekly profit of $321
d. A weekly profit of $314 is from 200 widgets
You decide to throw a party. You spent $150 on party supplies and hope to make back the money by charging $5 per
person to come. Find the equation that represents this is…
f (x) 
, where f (x) is the money you make,
and x is the number of people that come.
1. If 35 people came, would you make $40? In other words, does f (35)  40 ?
2. If 32 people came, would you make $10? In other words, does f (32)  10 ?
3. If no one came to the party, how much money would you make? In other words, find f (0) .
4. How many people would need to come for you to break even? In other words, find x such that f ( x)  0 .
5. How many people would need to come for you to make $100? In other words, find x such that f ( x)  100 .
6. Complete the following table. (Remember f ( x)  y !)
y ( x, y )
y
x
0
7. Plot the points and graph
y
400
0
10
50
100
300
200
100
x
10 30 50
-100
-200
8. What (x, y) coordinate is the x-intercept of this graph?
9. What (x, y) coordinate is the y-intercept of this graph?
10. What is the slope of this graph?
70
90
Answers:
You decide to throw a party. You spent $150 on party supplies and hope to make back the money by charging $5 per
person to come. Find the equation that represents this is…
f ( x)  5x  150 , where f (x) is the money you make,
and x is the number of people that come.
1. If 35 people came, would you make $40? In f (35)  5(35)  150
other words, does f (35)  40 ? NO!
 175  150
 25
f (32)  5(32)  150
2. If 32 people came, would you make $10? In
other words, does f (32)  10 ? YES!
 160  150
 10
3. If no one came to the party, how much money
would you make? In other words, find f (0) .
f (0)  5(0)  150
 0  150
 $  150
4. How many people would need to come for
0  5 x  150
 150  0  150
you to break even? In other words, find x such
that f ( x)  0 .
150  5 x
30 people  x
100  5 x  150
5. How many people would need to come for you to  150  0  150
make $100? In other words, find x such that
f ( x)  100 .
250  5 x
125 people  x
7. Plot the points and graph
6. Complete the following table. (Remember f ( x)  y !)
y
x
y  5x  150
( x, y)
0
-150
(0,
-150)
y  5(0)  150
30
(30, 0)
y  5(30)  150 0
10
y  5(10)  150 -100 (10, -100)
40
(40, 50)
y  5(40)  150 50
100 y  5(100)  150 350
(100, 350)
y
400
300
200
100
x
10 30 50
-100
-200
8. What (x, y) coordinate is the x-intercept of this graph?
(30, 0)
9. What (x, y) coordinate is the y-intercept of this graph?
(0, -150)
10. What is the slope of this graph?
The slope is 5.
70
90