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Questions and Answers
What is the slope of the equation y = 5x + 6?
What is the slope of the equation y = 5x + 6?
- 1
- 0
- 6
- 5 (correct)
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 (A)
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 + ___.
Match the following equations with their corresponding forms:
Match the following equations with their corresponding forms:
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?
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.
What do A and B represent in the equation Ax + By = C?
What do A and B represent in the equation Ax + By = C?
The rewritten form of 8x + 2y = -5 is y = ___x + ___.
The rewritten form of 8x + 2y = -5 is y = ___x + ___.
Match the equations with their slopes:
Match the equations with their slopes:
Flashcards
Rewrite 4x - y = 9 in y = mx + b form
Rewrite 4x - y = 9 in y = mx + b form
Isolate 'y' in the equation 4x - y = 9 to express it in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Rewrite 8x + 2y = -5 in y = mx + b form
Rewrite 8x + 2y = -5 in y = mx + b form
Rewrite the equation 8x + 2y = -5 in the format y = mx + b, solving for 'y' in terms of 'x'.
Rewrite 5x + 3y = -4 in y = mx + b form
Rewrite 5x + 3y = -4 in y = mx + b form
Transform the equation 5x + 3y = -4 into the slope-intercept form (y = mx + b).
Rewrite y = -7x + 4 in Ax + By = C form
Rewrite y = -7x + 4 in Ax + By = C form
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Rewrite y = 4x - 7 in Ax + By = C form
Rewrite y = 4x - 7 in Ax + By = C form
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Rewrite y = -7x + 3 in Ax + By = C form
Rewrite y = -7x + 3 in Ax + By = C form
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Rewrite 2y - 4 = -3x in y = mx + b form
Rewrite 2y - 4 = -3x in y = mx + b form
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Rewrite 5 + 3y = -4x in y = mx + b form
Rewrite 5 + 3y = -4x in y = mx + b form
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Rewrite 5 - 2x + y = 0 in y = mx + b form
Rewrite 5 - 2x + y = 0 in y = mx + b form
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Rewrite 3 - 6y - 3x = 2 in y = mx + b form
Rewrite 3 - 6y - 3x = 2 in y = mx + b form
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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
-
Example 1: 3x - 2y = 4 becomes y = (3/2)x - 2
- Isolating y: -2y = -3x + 4
- Dividing by -2: y = (3/2)x - 2
-
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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