Questions and Answers
Consider the line $y = \frac{2}{3}x - 4$. A line parallel to the graph of the line would have a slope of ____. A line perpendicular to the graph of the line would have a slope of ____.
Consider the line $y = \frac{2}{3}x - 4$. A line parallel to the graph of the line would have a slope of ____. A line perpendicular to the graph of the line would have a slope of ___.
2/3, -3/2
What is the slope of the line that is parallel to the y-axis and passes through the point (-1, 5)?
undefined
Which lines are parallel to the graph of $4x - y = 6$? (Select all that apply)
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Determine the slope-intercept form of the equation of the line parallel to $y = -\frac{4}{3} x + 11$ that passes through the point (-6, 2). $y = ___x + ___$
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Determine the equation of the line perpendicular to the line $y = -8$ through the point (-4, -2). The line $y = -8$ is _____. The line perpendicular to the line $y = -8$ is _____. The equation of the line perpendicular to the line $y = -8$ through the point (-4, -2) is ____.
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Are the lines perpendicular?
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Is triangle ABC a right triangle?
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A quadrilateral has vertices E(-4, 2), F(4, 7), G(8, 1), and H(0, -4). Which statements are true? (Select all that apply)
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For which value of a are the graphs of $-4 = 3x + 6y$ and $ax - 8y = 12$ parallel?
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Is the line $y = 3x - 7$ parallel or perpendicular to $3x + 9y = 9? Explain your answer.
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Study Notes
Equations of Parallel and Perpendicular Lines Study Notes
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A line parallel to (y = \frac{2}{3}x - 4) has a slope of (\frac{2}{3}); a perpendicular line has a slope of (-\frac{3}{2}).
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A line parallel to the y-axis is vertical and has an undefined slope, regardless of its passing point (e.g. through point ((-1, 5))).
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For the line defined by (4x - y = 6), parallel lines include:
- (y + 1 = 4(x - 2))
- (y = 4x + 11)
- (8x - 2y = 6)
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To determine the slope-intercept form of a line parallel to (y = -\frac{4}{3}x + 11) and passing through point ((-6, 2)), the equation is given as (y = -\frac{4}{3}x - 6).
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The line (y = -8) is horizontal; a line perpendicular to it is vertical. The equation passing through point ((-4, -2)) is (x = -4).
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Lines are not perpendicular if their slopes are not opposite reciprocals.
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Triangle ABC is a right triangle if one side is perpendicular to another, confirming that segment (BC) is perpendicular to (AC).
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For quadrilateral with vertices (E(-4, 2)), (F(4, 7)), (G(8, 1)), and (H(0, -4)):
- The slopes of (EF) and (GH) are both (\frac{5}{8}).
- Quadrilateral (EFGH) is a parallelogram because both pairs of opposite sides are parallel.
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For the equations (-4 = 3x + 6y) and (ax - 8y = 12) to be parallel, (a) must equal (-4).
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Lines (y = 3x - 7) and (3x + 9y = 9) are perpendicular because their slopes (3 and (-\frac{1}{3})) are opposite reciprocals, yielding a product of (-1).
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Description
This quiz covers the concepts of parallel and perpendicular lines, including their slopes and equations. It discusses specific examples and applications in determining the relationships between lines and angles in geometry. Ideal for students studying line equations in algebra.
