Unit 2: Graphing Equations
Lesson 8: Graphing Standard Form Equations – Lesson 1 of 2
A Close Look at Intercepts
The y-intercept is on the ________________.
The y-intercepts all have _______________
___________________________________.
The x-intercept is on the ________________.
The x-intercepts all have _______________
___________________________________.
Finding Intercepts
To find the y-intercept: ________________________
To find the x-intercept: ________________________
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Unit 2: Graphing Equations
Example 1
Graph the line:
4x – 3y = -24
X-intercept: (Let y = 0)
Y-intercept: (Let x = 0)
Example 2
Graph the line:
-2x - 9y = 18
X-intercept: (Let y = 0)
Y-intercept: (Let x = 0)
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Unit 2: Graphing Equations
Example 3
Find the x-intercept of the line: y = -3x – 2.
Example 4
Mary is preparing for a Super Bowl Party. She has $200 to spend on pizza and wings. One pizza
costs $10. One order of wings costs $5. The equation representing x pizzas and y orders of
wings is: 10x + 5y = 200
•
•
Graph the equation on the grid. Let x = the number of pizzas and y = the number of orders
of wings.
Using your graph, list one realistic option for buying pizza and wings.
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
Lesson 8: Graphing Standard Form Equations
1. Which line has an x intercept of 8 and a y intercept of 5?
A. Line A
B. Line B
C. Line C
D. None
HINT:
2.. Find the x intercept of the line: y = -3x -1
Let y = 0 to find the x-intercept.
A. -1
C. -1/3
B. -3
D. 1
3. Find the x intercept of the line: y = 2x +4
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Unit 2: Graphing Equations
4. The slope of a line is ½. The y- intercept is -3. Find the x-intercept.
5. Given the equation: 3x +6y = 9, find the x and y intercepts.
6. Graph the following equations on the grid provided.
A. -2x +8y = 16
B. x – 4y = 8
X intercept = __________
X intercept = __________
Y intercept = __________
Y intercept = __________
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Unit 2: Graphing Equations
7. John has started a summer business mowing grass. He charges $10 per hour, but had to spend
$50 on equipment. The equation, y = 10x – 50 is used to determine the total profit after mowing x
lawns.
•
•
•
Graph the equation on the grid. Let x = the number of hours worked. Let y = the profit.
Use your graph to determine the amount of profit for 10 hours. Justify your answer.
Explain why the y-intercept is a negative number in this problem.
Hint: Since the numbers in the equation are so
large, it will be easier to find the x and y
intercepts.
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Unit 2: Graphing Equations
8. Jerry spent $30 on ice cream and cookies for his children’s party. Ice cream costs $2 a cone and
cookies cost $1.50 a piece. The equation representing x ice cream cones and y cookies is
2x +1.50y = $30.
• Graph the equation on the grid. Let x = number of ice cream cones and y = number of
cookies.
• Suppose Jerry bought 6 ice cream cones, how many cookies can he buy for $30? Explain
your answer.
9. John is supplying hot dogs and sodas for the high school football game. He has $450 to spend.
The hot dogs cost $3 per pack of 6. The sodas cost $0.50 a piece. The equation representing x
hot dogs and y sodas is: 3x +.50y = 450.
• Graph the equation on the grid.
Let x = the number of hot dogs and
y = the number of sodas.
• Using your graph, list three different realistic options for buying hot dogs and sodas.
(For example, John could buy ____ packages of hot dogs and ____ sodas for $450).
Quiz #2 is next! You will need to be able to graph equations written in slope intercept form, find the
slope of a line given 2 points, and calculate rate of change. Don’t forget to create a study guide.
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Unit 2: Graphing Equations
1. The slope of a line is 5 and the y- intercept is -4. Find the x-intercept.
(2 points)
For problems 2-3, identify the x and y-intercepts. Then graph the equations on the grid (3 points ea)
2. 3x – 2y = 18
3. x + 3y = 9
x-intercept: __________
x-intercept: ________
y-intercept: __________
y-intercept: ________
4. Kerry is purchasing food and drinks for an annual Halloween party. She has a budget of $250
and she must provide appetizers and drinks for 40 people. Appetizers average about $9 per box
and sodas average $.90 a 2 liter bottle. Let x represent the number of boxes of appetizers and let y
= the number of 2 liter bottles of soda. The equation that represents this situation is: 9x + .90y =
250. (3 points)
• Graph the equation on the grid.
Let x = the number of appetizers and
y = the number of 2 liters of soda.
• Using your graph, list two different realistic options for buying appetizers and sodas.
(For example, Kerry could buy ____ packages of appetizers and ____ sodas for $250).
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
Lesson 8: Graphing Standard Form Equations– Answer Key
1. Which line has an x intercept of 8 and a y intercept of 5?
A. Line A
B.
B Line B
C. Line C
D. None
2.. Find the x intercept of the line: y = -3x -1
HINT:
You can use the same method to find
the x intercept even if the equation is
written in slope intercept form.
X intercept: Let y = 0
Let y = 0 to find the x-intercept.
y = -3x - 1
0 = -3x -1
0+1 = -3x -1 + 1
1 = -3x
1/-3 = -3x/-3
-1/3 = x
A. -1
C. -1/3
B. -3
D. 1
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Unit 2: Graphing Equations
3. Find the x intercept of the line: y = 2x +4
Let y = 0
Y = 2x + 4
0 = 2x + 4
0 – 4 = 2x + 4 -4
-4 = 2x
-4/2 = 2x /2
Substitute 0 for y.
Subtract 4 from both sides.
-2 = x
The X intercept is -2
Divide by 2 on both sides.
4. The slope of a line is ½. The y- intercept is -3. Find the x-intercept.
Since I know the slope and y intercept, I can write an equation in slope intercept form:
y = mx +b
m = slope (1/2) b = y intercept (-3)
y = 1/2x -3
Write the equation in slope intercept form.
0 = 1/2x – 3
Let y = 0 to find the x-intercept
0 +3 = 1/2x – 3 + 3
Add 3 to both sides.
3 = 1/2x
(2)3 = (2)1/2x
Multiply by 2 on both sides.
6=x
The x intercept is 6
5. Given the equation: 3x +6y = 9, find the x and y intercepts.
X intercept: Let y = 0
Y Intercept: Let x = 0
3x +6y = 9
3x +6y = 9
3x +6(0) = 9
3(0) +6y = 9
3x = 9
3 3
6y = 9
6
6
x =3
X intercept = 3
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y = 3/2
Y intercept = 3/2
Unit 2: Graphing Equations
6. Graph the following equations on the grid provided.
A. -2x +8y = 16
B. x – 4y = 8
X Intercept: y=0
Y Intercept: x=0
X intercept: y=0
y intercept: x=0
(Eliminates y term)
(Eliminates x term)
x=8
-2x = 16
-2
-2
8y = 16
8
8
-4y = 8
-4 -4
X = -8
y=2
y = -2
X intercept = ___-8_______
X intercept = ____8______
Y intercept = ____2______
Y intercept = _____-2_____
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
7. John has started a summer business mowing grass. He charges $10 per hour, but had to spend
$50 on equipment. The equation, y = 10x – 50 is used to determine the total profit after mowing x
lawns.
•
•
•
Graph the equation on the grid. Let x = the number of hours worked. Let y = the profit.
Use your graph to determine the amount of profit for 10 hours. Justify your answer.
Explain why the y-intercept is a negative number in this problem.
Since the equation is written in slope intercept form, we
know the y intercept is -50. Since this is a large number
and we know that we cannot use a scale of 1 on the
graph, it would be easiest to find the x intercept.
Y = 10x-50
0 = 10x – 50
Let y = 0
0 + 50 = 10x – 50 + 50
50 = 10x
50/10 = 10x/10
5=x
X intercept = 5
Y intercept = -50
**You need to establish your scale for the x and y axis.
Since the x intercept is 5, and you only need to
determine a profit for 10 hours, you can use a scale of 1.
Since the y intercept is -50, we can use a scale of 10.
• According to the graph, the amount of profit for 10 hours would be $50.
• Justify:
y = 10x-50
Original Equation
y = 10(10) – 50
Substitute 50 hours for x
y = 50
y is the profit, so our profit is $50.
• The y-intercept is a negative number in this problem because before John starts
working (0 hours), he has lost money. Since he had to buy equipment for $50, he is in
the negative. He would have to work 5 hours before breaking even at $0 and then he
will start making a profit.
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
8. Jerry spent $30 on ice cream and cookies for his children’s party. Ice cream costs $2 a cone and
cookies cost $1.50 a piece. The equation representing x ice cream cones and y cookies is
2x +1.50y = $30.
• Graph the equation on the grid. Let x = number of ice cream cones and y = number of
cookies.
• Suppose Jerry bought 6 ice cream cones, how many cookies can he buy for $30? Explain
your answer.
Since this equation is already written in standard form,
it is easiest to find the x and y intercepts in order to
graph this equation on the grid.
2x + 1.50y = 30
X Intercept: y = 0
0
Y Intercept: x =
2x + 1.50y = 30
2x + 1.50y = 30
2x + 1.50(0) = 30
2(0) +1.50y = 30
2x = 30
2
2
1.50y = 30
1.50 1.50
x = 15
X intercept = 15
y = 20
Y Intercept = 20
**I must choose a scale that will fit on my graph. I
chose to count by 2’s because then I can maximize the
space in my graph. This graph has endpoints at the x
and y intercept since it represents Jerry’s spending to
$30. It doesn’t go on until infinity like other graphs.
According to the graph, if Jerry bought 6 ice cream cones, he could buy 12 cookies for $30. The point on the
line with an x coordinate of 6 is (6, 12). That means 6 ice cream cones and 12 cookies can be purchased for
$30. Let’s prove it by substituting into the original equation.
2x + 1.50y = 30
2(6) +1.50(12) =
12 + 18 = 30
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
9. John is supplying hot dogs and sodas for the high school football game. He has $450 to spend.
The hot dogs cost $3 per pack of 6. The sodas cost $0.50 a piece. The equation representing x
hot dogs and y sodas is: 3x +.50y = 450.
• Graph the equation on the grid.
Let x = the number of hot dogs and
y = the number of sodas.
• Using your graph, list three different realistic options for buying hot dogs and sodas.
(For example, John could buy ____ packages of hot dogs and ____ sodas for $450).
Since this equation is already written in
standard form, it would be easiest to graph
using the x and y intercepts. We also know
that our endpoints on the graph are the x and
y intercept since John’s spending is limited to
$450.
3x + .50y = 450
X intercept: y = 0
Y intercept: x = 0
3x + .50y = 450
3x +.50y = 450
3x +.50(0) = 450
3(0) +.50y = 450
3x = 450
3
3
.50y = 450
.50 .50
x = 150
y = 900
I need to choose a scale for my graph based
on the x and y intercept. I have 10 spaces on
the horizontal axis and it must reach 150. I
am going to use a scale of 20 on the x axis.
The y axis must reach 900. So, I will need to
use a scale of 100.
With $450, John could buy:
50 packages of hot dogs and 600 sodas.
3x +.50y = 450
3(50) +.50(600) = 450
60 packages of hot dogs and 540 sodas.
3x +.50y = 450
3(60) +.50(540) = 450
80 packages of hot dogs and 420 sodas.
3x +.50y = 450
3(80) +.50(420) = 450
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
1. The slope of a line is 5 and the y- intercept is -4. Find the x-intercept. (2 points)
Slope = 5
Y-int = -4.
Equation in slope intercept form: y = 5x – 4
If we are finding the x-intercept, then we will let y = 0.
Y = 5x – 4
0 = 5x – 4
let y = 0
0+4 = 5x – 4+ 4
Add 4 to both sides
4 = 5x
Simplify
4/5 = 5x/5
Divide by 5 on both sides
4/5 = x
Simplify
The x-intercept is equal to 4/5.
For problems 2-3, identify the x and y-intercepts. Then graph the equations on the grid. (3 points
ea)
2. 3x – 2y = 18
3. x + 3y = 9
X-intercept:
Y-intercept:
X-intercept:
Y-intercept:
Let y = 0
Let x = 0
Let y = 0
Let x = 0
3x – 2(0) = 18
3(0)– 2y = 18
x +3(0) = 9
(0)+ 3y = 9
3x = 18
-2y = 18
x=9
3y = 9
3x/3 = 18/3
-2y/-2 = 18/-2
3y/3 = 9/3
x= 6
x= -9
x= 3
x-intercept: 6
x-intercept: 9
y-intercept: -9
y-intercept: 3
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
4. Kerry is purchasing food and drinks for an annual Halloween party. She has a budget of $250
and she must provide appetizers and drinks for 40 people. Appetizers average about $9 per box
and sodas average $.90 a 2 liter bottle. Let x represent the number of boxes of appetizers and let y
= the number of 2 liter bottles of soda. The equation that represents this situation is: 9x + .90y =
250.
(3 points)
• Graph the equation on the grid.
Let x = the number of appetizers and
y = the number of 2 liters of soda.
• Using your graph, list two different realistic options for buying appetizers and sodas.
(For example, Kerry could buy ____ packages of appetizers and ____ sodas for $250).
Find the x and y intercepts in order to graph the
equation on the grid.
X-intercept:
Y-intercept:
Let y = 0
Let x = 0
9x+.9(0) = 250
9(0)+.9y = 250
9x = 250
.9y = 250
9x/9 = 250/9
.9y/.9 = 250/.9
x= 27.8
y= 277.8
The x-intercept is 27.8 and the y-intercept is 277.8. Kerry could buy 21 boxes of appetizers
and 60 2-liters of soda. She could also buy 24 boxes of appetizers and 30 2-liters of soda.
(Answers may vary)
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