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Questions and Answers
What is the slope of the line represented by the equation $y = -\frac{1}{2}x + 4$?
What is the slope of the line represented by the equation $y = -\frac{1}{2}x + 4$?
- 1/2
- -1/2 (correct)
- 4
- 0
What point does the line $y = 4x + 8$ pass through?
What point does the line $y = 4x + 8$ pass through?
(−1, 4)
The line represented by $y = -\frac{5}{2}x + 2$ has a slope of -5/3.
The line represented by $y = -\frac{5}{2}x + 2$ has a slope of -5/3.
False (B)
Through which points does the line $y = -\frac{1}{2}x + 9$ pass?
Through which points does the line $y = -\frac{1}{2}x + 9$ pass?
What two points does the line $y = 5x - 2$ pass through?
What two points does the line $y = 5x - 2$ pass through?
Which equation is equivalent to $y = \frac{1}{4}x - 2$?
Which equation is equivalent to $y = \frac{1}{4}x - 2$?
Match the following equations with their forms:
Match the following equations with their forms:
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Study Notes
Point-Slope Form Overview
- Represents linear equations in the format y = mx + b, where m denotes the slope and b is the y-intercept.
- The slope represents the steepness of the line and direction (positive or negative).
Specific Linear Equations
-
y = -1/2x + 4
- Slope: -1/2
- Passes through the point (2, 3).
-
y = 4x + 8
- Slope: 4
- Passes through (-1, 4).
-
y = -5/2x + 2
- Slope: -5/2
- Passes through the y-intercept (0, 2).
-
y = -1/2x + 9
- Slope: -1/2
- Passes through multiple points: (-4, 6) and (-2, 5).
-
y = 5x - 2
- Slope: 5
- Passes through prominent points: (-1, -7) and (1, 3).
-
y = 1/4x - 2
- Can be expressed in point-slope form as: y + 5 = 1/4(x + 2).
-
y = 2x + 6
- Also can be rewritten as: y = 2(x + 3).
-
y = -3x + 5
- Expressed as: y - 8 = -3(x + 1).
-
y = -1/5x - 3
- Can be rearranged as: y + 3 = -1/5x.
General Concepts
- Each equation exemplifies the relationship between slope and specific points on the line.
- Point-slope form is useful for quickly identifying characteristics of linear equations, including slope direction and intersecting coordinates.
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