Questions and Answers
What is the solution for y in the equation -3x + 2y = 2?
What is the expression for y in the equation x - 4y = 8?
y = -x/-4 - 2
Express y from the equation 2x + y = -3.
y = 2x - 3
What is y in the equation 2x + 3y = 6?
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How do you express y in the equation 3x - y = 1?
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What is the expression for y in -3x - 5y = 10?
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In the equation 4x + 3y = 0, what is y?
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What is the value of y in the equation y - 3 = 0?
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Express y from the equation 2x - 3y = 9.
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What is the expression for y in the equation x + 2y - 4 = 0?
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Study Notes
Linear Equations and Their Forms
- Linear equations can be expressed in the standard form (Ax + By = C).
- Each equation can be rearranged to express (y) as a function of (x) in slope-intercept form (y = mx + b).
Example Equations and Their Manipulations
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Equation: (-3x + 2y = 2**
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Rearranged*: (y = \frac{3}{2} + 1)
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Equation: (x - 4y = 8**
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Rearranged*: (y = -\frac{x}{4} - 2)
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Equation: (2x + y = -3**
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Rearranged*: (y = 2x - 3)
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Equation: (2x + 3y = 6**
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Rearranged*: (y = -\frac{2}{3}x + 2)
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Equation: (3x - y = 1**
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Rearranged*: (y = 3x - 1)
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Equation: (-3x - 5y = 10**
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Rearranged*: (y = -\frac{3}{5}x - 2)
Special Values and Simplifications
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Equation: (4x + 3y = 0**
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Rearranged*: (y = -\frac{4}{3}x)
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Equation: (y - 3 = 0**
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Rearranged*: (y = 3) (This represents a horizontal line at (y = 3))
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Equation: (2x - 3y = 9**
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Rearranged*: (y = \frac{2}{3}x - 3)
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Equation: (x + 2y - 4 = 0**
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Rearranged*: (y = -\frac{1}{2}x + 2)
Important Concepts
- The slope-intercept form highlights the slope ((m)) and y-intercept ((b)) of the linear equation.
- A horizontal line has a constant (y) value, while vertical lines are represented by undefined slope.
- Understanding how to rearrange equations into slope-intercept form is crucial for graphing linear equations.
Studying That Suits You
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Description
Test your knowledge of Algebra 1 concepts with these flashcards focused on solving equations. Each card presents a linear equation and its corresponding definition, helping you learn how to manipulate and understand algebraic expressions. Perfect for reinforcing key algebra skills!
