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Questions and Answers
What is the equation for slope?
What is the equation for slope?
m = (y₂ - y₁) / (x₂ - x₁)
What is the slope-intercept form of a line?
What is the slope-intercept form of a line?
y = mx + b
What is the point-slope equation of a line?
What is the point-slope equation of a line?
y₂ - y₁ = m(x₂ - x₁)
The slopes of parallel lines are...
The slopes of parallel lines are...
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The slopes of perpendicular lines are...
The slopes of perpendicular lines are...
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If line y has slope -3/4, then a parallel line has slope...
If line y has slope -3/4, then a parallel line has slope...
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If line y has slope 1/3, then a perpendicular line has slope...
If line y has slope 1/3, then a perpendicular line has slope...
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Write the slope-intercept form of the equation of the line described through (2,0), parallel to y = 2/3x.
Write the slope-intercept form of the equation of the line described through (2,0), parallel to y = 2/3x.
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Write the slope-intercept form of the equation of the line described through (-2,4), parallel to y = -3/2x + 3.
Write the slope-intercept form of the equation of the line described through (-2,4), parallel to y = -3/2x + 3.
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Write the slope-intercept form of the equation of the line described through (4, 2), parallel to y = -3/4x - 5.
Write the slope-intercept form of the equation of the line described through (4, 2), parallel to y = -3/4x - 5.
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Write the slope-intercept form of the equation of the line described through (−3, −3), parallel to y = 7/3x + 3.
Write the slope-intercept form of the equation of the line described through (−3, −3), parallel to y = 7/3x + 3.
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Write the slope-intercept form of the equation of the line described through (2,4), perpendicular to y = -2/7x - 5.
Write the slope-intercept form of the equation of the line described through (2,4), perpendicular to y = -2/7x - 5.
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Write the slope-intercept form of the equation of the line described through (5,0), perpendicular to y = -x + 5.
Write the slope-intercept form of the equation of the line described through (5,0), perpendicular to y = -x + 5.
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Write the slope-intercept form of the equation of the line described through (−4, 0), perpendicular to y = 3/4x − 2.
Write the slope-intercept form of the equation of the line described through (−4, 0), perpendicular to y = 3/4x − 2.
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Write the slope-intercept form of the equation of the line described through (−1, 4), perpendicular to y = −5x + 2.
Write the slope-intercept form of the equation of the line described through (−1, 4), perpendicular to y = −5x + 2.
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Which of the following is an equation of a line that is perpendicular to line L which passes through the points (6,-1) and (-3,2)? (Select one)
Which of the following is an equation of a line that is perpendicular to line L which passes through the points (6,-1) and (-3,2)? (Select one)
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What is the slope of a line that is perpendicular to the line graphed in the standard coordinate plane?
What is the slope of a line that is perpendicular to the line graphed in the standard coordinate plane?
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What is the equation of line n, which is parallel to line m (3x - 2y = 8) and has a y-intercept that is 4 more than the y-intercept of m?
What is the equation of line n, which is parallel to line m (3x - 2y = 8) and has a y-intercept that is 4 more than the y-intercept of m?
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What describes two intersecting lines that are not perpendicular?
What describes two intersecting lines that are not perpendicular?
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Study Notes
Slope and Line Equations
- Slope formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} ) represents "rise over run."
- Slope-intercept form: ( y = mx + b ), where ( y ) is the dependent variable, ( x ) is the independent variable, ( m ) is the slope, and ( b ) is the y-intercept.
- Point-slope equation: ( y_2 - y_1 = m(x_2 - x_1) ) is used for finding the equation of a line using a point and slope.
Parallel and Perpendicular Lines
- Parallel lines have the same slope.
- Perpendicular lines have slopes that are negative reciprocals of each other; e.g. the slope of a line is ( m ), then a perpendicular line has a slope of ( -\frac{1}{m} ).
Example Slopes
- If a line has a slope of ( -\frac{3}{4} ), any parallel line will also have a slope of ( -\frac{3}{4} ).
- If a line has a slope of ( \frac{1}{3} ), a line perpendicular to it will have a slope of ( -3 ).
Finding New Lines
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To find the equation of a parallel line through a point:
- Identify the slope from an existing line.
- Use the point and slope to substitute into the slope-intercept form ( y = mx + b ).
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To find the equation of a perpendicular line:
- Determine the slope of the existing line, take its negative reciprocal.
- Substitute the new slope and the given point into the slope-intercept form to solve for ( b ).
Example Equations
- The equation ( y = \frac{2}{3}x - \frac{4}{3} ) is a line parallel to ( y = \frac{2}{3}x ) that passes through the point (2, 0).
- The equation ( y = -\frac{3}{2}x + 1 ) results from a line with a point (-2, 4) parallel to ( y = -\frac{3}{2}x + 3 ).
- The equation ( y = -\frac{4}{3}x - \frac{16}{3} ) is perpendicular to the line ( y = \frac{3}{4}x - 2 ) through point (-4, 0).
Advanced Concepts
- Evaluate if two lines intersect perpendicularly or are parallel based on their slopes.
- Identify perpendicular slopes: a line with slope ( -\frac{5}{3} ) will need a corresponding line with a slope of ( \frac{3}{5} ) for perpendicularity.
- Solve for equations of lines through specific points with given conditions regarding slopes.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of key algebra concepts with these flashcards focusing on the slope and the equations of lines. Each card provides a definition and asks for the corresponding equation or concept. Perfect for reviewing the core principles of Algebra 1.
