Algebra 1 Flashcards (3.4)

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Questions and Answers

What is the solution for y in the equation -3x + 2y = 2?

  • y = 2 - 3x/2
  • y = 3/2 + 1 (correct)
  • y = -2 + 3x/2
  • y = -3x/2 + 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?

<p>y = -2x/3 + 2</p> Signup and view all the answers

How do you express y in the equation 3x - y = 1?

<p>y = -3x/-1 - 1</p> Signup and view all the answers

What is the expression for y in -3x - 5y = 10?

<p>y = 3x/-5 - 2</p> Signup and view all the answers

In the equation 4x + 3y = 0, what is y?

<p>y = -4/3 + 0</p> Signup and view all the answers

What is the value of y in the equation y - 3 = 0?

<p>y = 3</p> Signup and view all the answers

Express y from the equation 2x - 3y = 9.

<p>y = -2/-2 - 3</p> Signup and view all the answers

What is the expression for y in the equation x + 2y - 4 = 0?

<p>y = -x/2 + 2</p> Signup and view all the answers

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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

  • Equation: (-3x + 2y = 2**

  • Rearranged*: (y = \frac{3}{2} + 1)

  • Equation: (x - 4y = 8**

  • Rearranged*: (y = -\frac{x}{4} - 2)

  • Equation: (2x + y = -3**

  • Rearranged*: (y = 2x - 3)

  • Equation: (2x + 3y = 6**

  • Rearranged*: (y = -\frac{2}{3}x + 2)

  • Equation: (3x - y = 1**

  • Rearranged*: (y = 3x - 1)

  • Equation: (-3x - 5y = 10**

  • Rearranged*: (y = -\frac{3}{5}x - 2)

Special Values and Simplifications

  • Equation: (4x + 3y = 0**

  • Rearranged*: (y = -\frac{4}{3}x)

  • Equation: (y - 3 = 0**

  • Rearranged*: (y = 3) (This represents a horizontal line at (y = 3))

  • Equation: (2x - 3y = 9**

  • Rearranged*: (y = \frac{2}{3}x - 3)

  • Equation: (x + 2y - 4 = 0**

  • 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.

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