Podcast
Questions and Answers
What is the slope of the equation y = 5x + 6?
What is the slope of the equation y = 5x + 6?
In the equation Ax + By = C, for A to be positive, it cannot be a fraction.
In the equation Ax + By = C, for A to be positive, it cannot be a fraction.
True
What is the y-intercept of the equation y = -3x + 7?
What is the y-intercept of the equation y = -3x + 7?
7
The equation 2y - 8 = -4x can be rewritten as y = ___x + ___.
The equation 2y - 8 = -4x can be rewritten as y = ___x + ___.
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Match the following equations with their corresponding forms:
Match the following equations with their corresponding forms:
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Which of the following representations shows the correct rearranging of the equation y = 2x - 5 into the form Ax + By = C?
Which of the following representations shows the correct rearranging of the equation y = 2x - 5 into the form Ax + By = C?
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The equation 5 - 3y = 2x can be directly rewritten to the form y = mx + b.
The equation 5 - 3y = 2x can be directly rewritten to the form y = mx + b.
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What do A and B represent in the equation Ax + By = C?
What do A and B represent in the equation Ax + By = C?
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The rewritten form of 8x + 2y = -5 is y = ___x + ___.
The rewritten form of 8x + 2y = -5 is y = ___x + ___.
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Match the equations with their slopes:
Match the equations with their slopes:
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Study Notes
Rewriting Linear Equations
- Linear equations can be written in two forms: Ax + By = C and y = mx + b
- The form Ax + By = C is standard form (A, B, and C are constants, and A should be positive).
- The form y = mx + b is slope-intercept form. (m is the slope and b is the y-intercept)
- Rewriting from Ax + By = C to y = mx + b involves isolating y by performing operations on both sides of the equation
- Rewriting from y = mx + b to Ax + By = C involves moving variables and constants to organize the equation in standard form
Illustrative Examples
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Example 1: 3x - 2y = 4 becomes y = (3/2)x - 2
- Isolating y: -2y = -3x + 4
- Dividing by -2: y = (3/2)x - 2
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Example 2: y = 5x + 6 becomes -5x + y = 6
- Rewriting using properties of real numbers: -5x + y = 6
Activity A
- The activity involves rewriting equations from the form Ax + By = C to y = mx + b and vice versa (finding the slope and y-intercept)
- Examples are provided for rewriting various linear equations
Activity B
- The activity involves rewriting equations from the form y = mx + b to Ax + By = C
- Examples cover different slope and y intercept values.
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Description
This quiz focuses on rewriting linear equations between standard form and slope-intercept form. It includes explanations and examples, providing an interactive activity for practice. Test your skills in transforming equations and finding slopes and intercepts.
