Podcast
Questions and Answers
What is the slope of a line that passes through the points (1, 2) and (4, 5)?
What is the slope of a line that passes through the points (1, 2) and (4, 5)?
If a line has a slope of 2, what is the slope of a line that is perpendicular to it?
If a line has a slope of 2, what is the slope of a line that is perpendicular to it?
Which of the following equations represents a line parallel to y = 3x + 2?
Which of the following equations represents a line parallel to y = 3x + 2?
What is the midpoint of the points (2, 3) and (4, 7)?
What is the midpoint of the points (2, 3) and (4, 7)?
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What is the slope of a line that is parallel to a line with a slope of -4?
What is the slope of a line that is parallel to a line with a slope of -4?
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Study Notes
Slope
- Slope is calculated as rise over run (change in y over change in x)
- Formula: m = (y₂ - y₁) / (x₂ - x₁)
- Example: For points (3, 4) and (-2, 7), the slope is (7 - 4) / (-2 - 3) = 3 / -5 = -3/5
Parallel Lines
- Parallel lines have the same slope
- Example: A line parallel to a line with slope -3 has a slope of -3
Perpendicular Lines
- Perpendicular lines have slopes that are opposite reciprocals
- Example: A line perpendicular to a line with slope 2/3 has a slope of -3/2
Slope-intercept Form
- Equation: y = mx + b
- Where:
- m = slope
- b = y-intercept (the point where the line crosses the y-axis)
Point-slope Form
- Equation: y - y₁ = m(x - x₁)
- Where:
- m = slope
- (x₁, y₁) = a point on the line
Example Equation Problems
-
Find an equation of a line parallel to y = -2x + 4 that passes through (0, -5)
- The slope is -2
- The y-intercept is -5
- Equation: y = -2x - 5
-
Find the equation of the perpendicular bisector of a line segment JM, where J = (-6, 4) and M = (8, 10)
- Calculate the slope of JM: m = (10 - 4) / (8 - (-6)) = 6/14 = 3/7
- Calculate the midpoint of JM: ((-6 + 8)/2, (4 + 10)/2) = (1, 7)
- Calculate the slope of the perpendicular line: -7/3
- Use the point-slope form with the midpoint and the new slope: y - 7 = -7/3(x - 1)
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Description
Test your understanding of slope, parallel and perpendicular lines, and line equations. This quiz covers concepts like slope-intercept form and point-slope form with practical examples. Challenge yourself with problems involving finding equations of lines based on slope.
