Unit 3: Writing Equations
Lesson 2: Writing Equations in Standard Form
Standard Form
Special Rule #1 for Standard Form:
The lead coefficient (A) must be _______________________________.
Example 1
Rewrite the equation y = 6x – 8 in standard form.
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Unit 3: Writing Equations
Special Rule #2 for Standard Form:
Equations that are written in standard form CANNOT contain _____________________________.
Ax + By = C
A, B, and C must be ___________________________.
Example 2
Rewrite the equation y = 1/3x +
½ in standard form.
Step 1: Multiply all terms by ____ in order to get rid of the fractions.
Step 2: Write the equation in standard form.
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Unit 3: Writing Equations
Lesson 2: Writing Equations in Standard Form
1. Rewrite the equation y = 3x -5 in standard form.
A.
B.
C.
D.
3x+y = -5
3x -y = 5
-3x –y = -5
3x+y = 5
2. Rewrite the equation y = -2x +6 in standard form.
3. Rewrite the equation y = 8x in standard form.
4. In the equation 2x +1/2y = 7, which term does not have an integer coefficient?
A.
B.
C.
D.
2x
1/2y
7
None of the above.
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Unit 3: Writing Equations
5. Write the equation y = -2/3x +2 in standard form with integer coefficients.
Step 1: Multiply all terms by _____ in order to get rid of the fraction.
Step 2: Write the equation in standard form.
A.
B.
C.
D.
2x +3y = 6
-2x +3y = 6
2/3x +y = 2
2x +y = 2
6. Write the equation y = 3/4x -5 in standard form with integer coefficients.
Step 1: Multiply all terms by _____ in order to get rid of the fraction.
Step 2: Write the equation in standard form.
7. Write the equation y = -3/5x – 2 in standard form with integer coefficients.
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Unit 3: Writing Equations
8. Which equation represents y = 1/2x +3/4 in standard form with integer coefficients?
Step 1: Multiply all terms by _____ in order to get rid of the fractions.
Step 2: Write the equation in standard form.
A.
B.
C.
D.
9.
10.
2x+4y = 3
x + 4y = 3
2x -4y = -3
-2x +y = 3
Write the equation y = -2/3x +5/6 in standard form.
Write the equation y = 3/4x +3/8 in standard form.
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Unit 3: Writing Equations
11. Write the equation (in standard form) that represents the line on the graph.
12.
Write the equation (in standard form) that represents the line on the graph.
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Unit 3: Writing Equations
Part 1: Rewrite each equation in standard
form with only integer coefficients. (2 points each)
1. y = 4x – 3
2. y = - ¾ x + 5
3. y = 1/2x – 2/3
Part 2: Write an equation in standard form that represents the line on the graph. (3 points)
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Unit 3: Writing Equations
Lesson 2: Writing Equations in Standard Form – Answer Key
1. Rewrite the equation y = 3x -5 in standard form.
y = 3x -5
-3x + y = 3x – 3x -5
Subtract 3x from both sides
-3x + y = -5
-1[-3x +y = -5]
Multiply all terms by -1 to make the lead
3x -y = 5
coefficient positive
A.
3x+y = -5
B. 3x -y = 5
C. -3x –y = -5
D. 3x+y = 5
2. Rewrite the equation y = -2x +6 in standard form.
y = -2x +6
2x +y = -2x +2x +6
Add 2x to both sides.
2x +y = 6
Equation written in standard form.
3. Rewrite the equation y = 8x in standard form.
y = 8x
y-y = 8x –y
Subtract y from both sides.
0 = 8x –y or 8x – y = 0
Equation written in standard form.
4. In the equation: 2x +1/2y = 7, which term does not have an integer coefficient?
½ is the coefficient of y, but it is not an integer. It is a fraction. You cannot have
fractions in your standard form equations.
A. 2x
B. 1/2y
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C. 7
D. None of the above.
Unit 3: Writing Equations
5. Write the equation y = -2/3x +2 in standard form with integer coefficients.
Step 1: Multiply all terms by 3 in order to get rid of the fraction.
3[y = -2/3x +2]
Tip: You can eliminate B and C
3y = -2x +6
from your answers.
B. Has a lead coefficient that is
negative. It must be positive.
Step 2: Write the equation in standard form.
3y = -2x +6
C. Has a coefficient that is a
fraction, and it must be an
integer.
2x +3y = -2x +2x + 6
Add 2x to both sides.
2x +3y = 6
Equation in standard form.
A. 2x +3y = 6
B. -2x +3y = 6
C. 2/3x +y = 2
D. 2x +y = 2
6. Write the equation y = 3/4x -5 in standard form with integer coefficients.
Step 1: Multiply all terms by 4 in order to get rid of the fraction.
4[y = 3/4x – 5]
4y = 3x - 20
Step 2: Write the equation in standard form.
4y = 3x - 20
-3x + 4y =3x – 3x -20
Subtract 3x from both sides.
-3x +4y = -20
-1[-3x +4y = -20]
3x -4y = 20
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Multiply all terms by -1 to make the lead
coefficient positive.
Equation written in standard form.
Unit 3: Writing Equations
7. Write the equation y = -3/5x – 2 in standard form with integer coefficients.
y = -3/5x - 2
5[y= -3/5x – 2]
Multiply all terms by 5 to get rid of the fraction.
5y = -3x -10
3x +5y = -3x +3x – 10
Add 3x to both sides.
3x +5y = -10
Equation written in standard form.
8. Which equation represents y = 1/2x +3/4 in standard form with integer coefficients?
Step 1: Multiply all terms by
4[y = 1/2x +3/4]
4y = 2x +3
4
in order to get rid of the fractions.
Step 2: Write the equation in standard form.
4y = 2x +3
-2x + 4y = 2x – 2x +3
Subtract 2x from both sides.
-2x +4y = 3
-1[-2x +4y = 3]
Multiply all terms by -1 to make the lead
coefficient positive.
2x – 4y = -3
A.
B.
C.
D.
2x+4y = 3
x + 4y = 3
2x -4y = -3
-2x +y = 3
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Equation written in standard form.
Unit 3: Writing Equations
9. Write the equation y = -2/3x +5/6 in standard form.
6[y = -2/3x + 5/6]
Multiply all terms by 6 to get rid of the fractions.
6y = -4x +5
4x +6y =-4x +4x + 5
Add 4x to both sides.
4x +6y = 5
Equation written in standard form.
10. Write the equation y = 3/4x +3/8 in standard form.
8[y = 3/4x +3/8]
Multiply all terms by 8 to get rid of the fractions.
8y = 6x +3
-6x +8y = 6x -6x +3
Subtract 6x from both sides.
-6x +8y = 3
-1[-6x +8y = 3]
Multiply all terms by -1 to make the lead
coefficient positive.
6x – 8y = -3
Equation written in standard form.
11. Write the equation (in standard form) that represents the line on the graph.
1. Write the equation in slope intercept form:
Slope (m) = 3/4
Y-intercept (b) = 3
y= mx +b
y = 3/4x + 3
2. Get rid of the fraction by multiplying every term by 4.
4[y = 3/4x + 3]
4y=3x +12
3. Move the x term to the left side by subtracting 3x from
both sides.
-3x +4y = 3x -3x +12
-3x +4y = 12
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4. Multiply all terms by -1 to make the lead coefficient
positive.
-1[-3x +4y = 12]
3x -4y = -12
Unit 3: Writing Equations
12. Write the equation (in standard form) that represents the line on the graph.
1. Write the equation in slope intercept form:
Slope (m) = -2/3
Y-intercept (b) = -3
y= mx +b
y = -2/3x - 3
2. Get rid of the fraction by multiplying every term by 3.
3[y = -2/3x - 3]
3y= -2x -9
3. Move the x term to the left side by adding 2x to both
sides.
2x+3y = -2x+ 2x -9
2x +3y = -9
Part 1: Rewrite each equation in standard form with
only integer coefficients. (2 points each)
1. y = 4x – 3
In order to rewrite the equation in standard form, we must have the variables, x and y on the same
side and the constant on the opposite side: Ax + By = C
-4x + y = 4x- 4x – 3
Subtract 4x from both sides
-4x + y = - 3
Simplify
-1(-4x + y) = -3(-1)
Multiply all terms by -1
4x – y = 3
Simplify
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Unit 3: Writing Equations
2. y = - ¾ x + 5
Start by getting rid of the fraction by multiplying all terms by 4.
4(y) = 4(-3/4x+5)
4y = -3x + 20
Simplify
Now we want x and y to be on the same side and the constant, 20 to be on the opposite side.
4y + 3x = -3x +3x +20
Add 3x to both sides
4y +3x = 20 or 3x +4y = 20
Simplify and rewrite with variables in order.
3x +4y = 20
Final answer
3. y = 1/2x – 2/3
In order to get rid of the fraction, we must multiply by 6 on both sides
6(y) = 6[1/2x – 2/3]
6y = 3x – 4
-3x + 6y = 3x-3x – 4
Subtract 3x from both sides
-3x + 6y = -4
Simplify
-1[-3x + 6y] = -4(-1)
Multiply by -1 to make the lead coefficient positive.
3x -6y = 4
Simplify: Final answer
Part 2: Write an equation in standard form that represents the line on the graph. (3 points)
It’s easiest to first write the equation in slope intercept form and
then rewrite it in standard form.
We can see that the y-intercept is -2, and the slope is -1/2, so…
m = -1/2
b = -2
y = mx + b
y = -1/2x -2 is the equation in slope intercept form
Now, rewrite in standard form. Let’s start by getting rid of the
fraction. We’ll multiply all terms by 2.
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2(y) = 2(-1/2x -2)
Multiply by 2.
2y = -x – 4
Simplify
2y +x = -x+x – 4
Add x to both sides.
2y +x = -4
Simplify
x + 2y = -4
Standard form equation.