Unit 2: Graphing Equations
Lesson 9: Graphing Standard Form Equations – Lesson 2 of 2
Method 2: Rewriting the equation in slope intercept form
Use the same strategies that were used for solving equations:
1. ______________________________________________________________
2. ______________________________________________________________
Your goal is to solve for _______________.
Example 1
Graph the following equations:
6x – 8y = -16
x – y = -9
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Unit 2: Graphing Equations
Lesson 9: Graphing an Equation in Standard Form (2 of 2)
Directions: First rewrite each equation in slope intercept form. Then identify the slope and yintercept. Last, graph your equation on the grid.
1. -4x – y = -2
Slope = ____
2. -2x – 3y = 6
y-intercept = ____
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Slope = ____
y-intercept = ____
Unit 2: Graphing Equations
3. -4x – y = -2
Slope = ____
4. -3x +9y = -9
y-intercept = ____
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Slope = ____
y-intercept = ____
Unit 2: Graphing Equations
5. Which one of the following equations shows 12x – 3y = 6 in slope intercept form?
A. 3y = 12x -6
B. y = 4x -2
C. –y = -4x + 2
D. y = 4x +2
6. Write an equation (in slope intercept form) that is equivalent to: 8x -2y = 12
7. Which one of the following equations shows -3y = 6 – 12x in slope intercept form?
A. -3y = 6 – 12x
B. y = 6 – 12x
C. y = 4x – 2
D. y = -4x + 2
8. Given the following equation: 3x – 5y = 10, identify the slope of the line.
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Unit 2: Graphing Equations
9. Given the following equation: 3x – 8y = 16, identify the slope and y-intercept of the line.
10. Are the following equations equivalent? Justify your answer.
2x – 4y = 8
&
y = -1/2x -2
1. Write an equation in slope intercept form that is equivalent to: 2x – 5y = 12
(2 points)
2. Given the equation: 4x + 3y = 8. Identify the slope and y-intercept of the line. (2 points)
3. Are the following equations equivalent? Explain your answer, then justify by graphing each line
on the grid below. (4 points)
2x – 3y = 15
4x = 6y + 36
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
Lesson 9: Graphing an Equation in Standard Form – Answer Key
Directions: For each problem below, identify the slope and the y-intercept.
1. 3x +2y = -4
2. -2x – 3y = 6
3x – 3x +2y = -4 – 3x
Subtract 3x
2y = -4 – 3x
2
2
Divide by 2
2
-2x +2x – 3y = 6 +2x
-3y = 6 +2x
-3
y = -2 - 3x
Simplify
Add 2x
Divide by -3
-3 -3
y = -2 – 2/3x
Simplify
y = -2/3x – 2
Switch terms around
2
y = -3/2x -2
Switch terms around
Slope = -2/3
Slope = -3/2
y-intercept = -2
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y-intercept = -2
Unit 2: Graphing Equations
3. -4x – y = -2
4. -3x +9y = -9
-4x +4x –y = -2 +4x
Add 4x
-y = -2 +4x
-1
Divide by -1
-1 -1
Add 3x
9y = -9 + 3x
Divide by 9
9
y = 2 – 4x
y = -4x +2
-3x +3x +9y = -9 +3x
Simplify
Switch terms around
9
9
y = -1 + 1/3x
y = 1/3 x – 1
Slope = 1/3
Slope = -4
y-intercept = 2
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Simplify
Switch terms around
y-intercept = -1
Unit 2: Graphing Equations
5. Which one of the following equations shows 12x – 3y = 6 in slope intercept form?
A. 3y = 12x -6
You can eliminate A and C immediately because slope
intercept form must by y = . The y cannot have a coefficient,
nor can it be negative. Eliminating answers that do not
make sense is a great test taking strategy!
B. y = 4x -2
C. –y = -4x + 2
12x – 3y = 6
D. y = 4x +2
12x -12x -3y = 6 – 12x
-3y = -12x +6
-3
-3 -3
y = 4x -2 - The answer is B
6. Write an equation (in slope intercept form) that is equivalent to: 8x -2y = 12
8x -8x – 2y = 12 -8x
Subtract 8x from both sides
-2y = -8x + 12
Simplify & reverse the terms on the right hand side.
-2y = -8x + 12
-2
-2
-2
Divide all terms by -2
y = 4x – 6
The equation written in slope intercept form.
7. Which one of the following equations shows -3y = 6 – 12x in slope intercept form?
A. -3y = 6 – 12x
B. y = 6 – 12x
C. y = 4x – 2
D. y = -4x + 2
You can eliminate letter A, because slope intercept form must be solved for y.
This equation is almost in slope intercept form. We must get y by itself on the left
hand side; therefore, we need to get rid of the coefficient of -3.
-3y = 6 – 12x
-3
-3 -3
y = -2 + 4x
Divide all terms by -3
OR y = 4x – 2
Equation written in slope intercept form.
8. Given the following equation: 3x – 5y = 10, identify the slope of the line.
In order to find the slope, we must rewrite the equation in slope intercept form.
3x -3x -5y = 10 -3x
-5y = -3x + 10
Subtract 3x from both sides
Simplify & reverse the terms on the right hand side.
-5y = -3x + 10
-5
-5
-5
Divide all terms by -5
y = 3/5x - 2
Equation written in slope intercept form.
The
slope
of
the
line
is
3/5.
(3/5
is
the
coefficient
of x, therefore, it is the slope)
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Unit 2: Graphing Equations
9. Given the following equation: 3x – 8y = 16, identify the slope and y-intercept of the line.
3x -3x – 8y = 16 – 3x
-8y = -3x + 16
-8y = -3x + 16
-8
-8
Subtract 3x from both sides.
Simplify & reverse the terms on the right hand side.
Divide all terms by -8
-8
y = 3/8x – 2
Equation written in slope intercept form.
The slope of the line is 3/8 and the y-intercept is -2.
10. Are the following equations equivalent? Justify your answer.
2x – 4y = 8
&
y = -1/2x -2
In order to determine if the equations are equivalent, you must rewrite the standard form in slope intercept
form. If the equations are equivalent, then they will be the exact same equation when written in slope
intercept form.
Let’s rewrite the standard form equation in slope intercept form.
2x – 4y = 8
2x -2x – 4y = 8 -2x
Subtract 2x from both sides.
-4y = -2x + 8
Simplify & reverse the terms on the right hand side.
-4y = -2x + 8
-4
-4 -4
Divide all terms by -4
y = 1/2x - 2
Equation written in slope intercept form.
The equations are not equivalent.
y = 1/2x -2 & y = -1/2x – 2 differ because equation #1 has a positive slope and equation #2 has a
negative slope.
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
1. Write an equation in slope intercept form that is equivalent to: 2x – 5y = 12 (2 points)
In order to write the equation in slope intercept form, I must solve for y.
2x – 5y = 12
Original equation
2x – 2x – 5y = 12 – 2x
Subtract 2x from both sides
-5y = -2x + 12
Simplify and rewrite in correct format
-5y/-5 = -2x/-5 + 12/-5
Divide ALL terms by -5
y = 2/5x – 12/5
Simplify
The equation in slope intercept form is: y = 2/5x – 12/5
2. Given the equation: 4x + 3y = 8. Identify the slope and y-intercept of the line. (2 points)
In order to identify the slope and y-intercept of the line, we must rewrite the equation in slope
intercept form. Therefore, we must solve for y.
4x + 3y = 8
Original equation
4x – 4x + 3y = 8 – 4x
Subtract 4x from both sides
3y = -4x + 8
Simplify and rewrite in correct format
3y/3 = -4x/3 + 8/3
Divide ALL terms by 3
y = -4/3x + 8/3
Simplify
The equation in slope intercept form is: y = -4/3x + 8/3. Therefore, the slope is -4/3 and the yintercept is 8/3.
Copyright© 2009 Algebra-class.com
Unit 2: Graphing Equations
3. Are the following equations equivalent? Explain your answer, then justify by graphing each line
on the grid below. (4 points)
2x – 3y = 15
4x = 6y + 36
We can tell if the equations are equivalent by rewriting both
in slope intercept form:
2x – 3y = 15
Original equation
2x-2x – 3y = 15 – 2x
Subtract 2x from both sides
-3y = -2x + 15
Simplify
-3y/-3 = -2x/-3 + 15/-3
Divide All terms by -3
y = 2/3x – 5
Equation in slope intercept form
4x = 6y +36
Original equation
4x – 36= 6y + 36 -36
Subtract 36 from both sides
4x – 36 = 6y
Simplify
4x/6 – 36/6 = 6y/6
Divide All terms by 6
2/3x – 6 = y
Equation in slope intercept form
y = 2/3x - 6
These equations are not equivalent because when written in slope intercept form, they are
not the same exact equation. The graph shows parallel lines, which means that the
equations are not equivalent. They have the same slope but different y-intercepts and this is
why they are parallel.
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