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Questions and Answers
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-2); y=-x-2
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-2); y=-x-2
y=-x
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-1); y=-3/2x+6
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-1); y=-3/2x+6
y=-3/2x+2
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (4,2); x=-3
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (4,2); x=-3
x=4
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (-2,3); y=1/2x-1
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (-2,3); y=1/2x-1
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Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (5,0); y+1=2(x-3)
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (5,0); y+1=2(x-3)
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Determine whether the graphs of the given equations are parallel, perpendicular, or neither: y=x+11 and y=-x+2.
Determine whether the graphs of the given equations are parallel, perpendicular, or neither: y=x+11 and y=-x+2.
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Determine whether the graphs of the given equations are parallel, perpendicular, or neither: y=-2x+3 and 2x+y=7.
Determine whether the graphs of the given equations are parallel, perpendicular, or neither: y=-2x+3 and 2x+y=7.
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Determine whether the graphs of the given equations are parallel, perpendicular, or neither: y=4x-2 and -x+4y=0.
Determine whether the graphs of the given equations are parallel, perpendicular, or neither: y=4x-2 and -x+4y=0.
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Determine whether the statement is always, sometimes, or never true: Two lines with positive slopes are parallel.
Determine whether the statement is always, sometimes, or never true: Two lines with positive slopes are parallel.
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Determine whether the statement is always, sometimes, or never true: Two lines with the same slope and different y-intercepts are perpendicular.
Determine whether the statement is always, sometimes, or never true: Two lines with the same slope and different y-intercepts are perpendicular.
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Study Notes
Parallel Lines
- Parallel lines have the same slope and will never intersect.
- For point (2, -2) and line equation y = -x - 2, the parallel line's slope remains -1, resulting in the equation y = -x.
- For point (2, -1) and line equation y = -3/2x + 6, the parallel line has a slope of -3/2, leading to y = -3/2x + 2.
- A vertical line (x = -3) has a parallel line at x = 4, as all vertical lines are parallel to each other.
Perpendicular Lines
- Perpendicular lines have slopes that are negative reciprocals of each other.
- For point (-2, 3) and line y = 1/2x - 1, the slope is 1/2, so the perpendicular slope is -2, resulting in the equation y = -2x - 1.
- For point (5, 0) and line equation y + 1 = 2(x - 3), the slope of the given line is 2, leading to the perpendicular slope of -1/2, creating the equation y = -1/2x + 5/2.
Relationship of Graphs
- Two equations y = x + 11 and y = -x + 2 are perpendicular due to slopes of 1 and -1.
- The equations y = -2x + 3 and 2x + y = 7 represent parallel lines with a slope of -2.
- The equations y = 4x - 2 and -x + 4y = 0 are neither parallel nor perpendicular, with different slopes.
General Statements about Slopes
- The statement "Two lines with positive slopes are parallel" is categorized as sometimes true, as they could intersect at certain angles.
- The statement "Two lines with the same slope and different y-intercepts are perpendicular" is never true, as this configuration describes parallel lines instead.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of parallel and perpendicular lines with this set of flashcards. Each card presents a point and a given equation, inviting you to write a corresponding equation in slope-intercept form. Perfect for reinforcing your skills in coordinate geometry!
