Questions and Answers
What is the equation for slope?
m = (y₂ - y₁) / (x₂ - x₁)
What is the slope-intercept form of a line?
y = mx + b
What is the point-slope equation of a line?
y₂ - y₁ = m(x₂ - x₁)
The slopes of parallel lines are...
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The slopes of perpendicular lines are...
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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...
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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.
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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.
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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.
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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.
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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.
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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)
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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?
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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
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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.
