Podcast
Questions and Answers
What is the slope between the points (-4, -6) and (3, 8)?
What is the slope between the points (-4, -6) and (3, 8)?
- 14/7
- 5/7 (correct)
- 2
- 3
Determine the slope between the points (-6, -2) and (3, 4).
Determine the slope between the points (-6, -2) and (3, 4).
- 7/9
- 1/3
- 2 (correct)
- 5/9
What is the slope of the line passing through the points (1, -8) and (3, -7)?
What is the slope of the line passing through the points (1, -8) and (3, -7)?
- -1
- 10
- 1/2
- 1 (correct)
Find the slope between the points (2, -2) and (8, 1).
Find the slope between the points (2, -2) and (8, 1).
What is the slope of the line that goes through points (-12, 4) and (0, 2)?
What is the slope of the line that goes through points (-12, 4) and (0, 2)?
Calculate the slope for points (6, 6) and (4, -7).
Calculate the slope for points (6, 6) and (4, -7).
What is the slope of the line passing through (-4, -5) to (4, 13)?
What is the slope of the line passing through (-4, -5) to (4, 13)?
What is the slope between the points (3, 1) and (9, -7)?
What is the slope between the points (3, 1) and (9, -7)?
What is the slope of the line given by the equation $5x + 3y = -21$?
What is the slope of the line given by the equation $5x + 3y = -21$?
What is the slope of the line that is perpendicular to the line $5x + 3y = -21$?
What is the slope of the line that is perpendicular to the line $5x + 3y = -21$?
What is the equation of the line that passes through the point (-5, 1) and is perpendicular to $5x + 3y = -21$?
What is the equation of the line that passes through the point (-5, 1) and is perpendicular to $5x + 3y = -21$?
Which point would create a line that is parallel to the equation $y = 2x + 4$?
Which point would create a line that is parallel to the equation $y = 2x + 4$?
If you write the equation of the line in slope-intercept form that passes through point (3, -3) and has a slope of 1, what is the equation?
If you write the equation of the line in slope-intercept form that passes through point (3, -3) and has a slope of 1, what is the equation?
What is the resulting equation of the line through the point (2, 3) parallel to the line $2x + 10y = 20$?
What is the resulting equation of the line through the point (2, 3) parallel to the line $2x + 10y = 20$?
What is the y-intercept of the line that is perpendicular to $y = -x + 7$ and passes through the point (8, 3)?
What is the y-intercept of the line that is perpendicular to $y = -x + 7$ and passes through the point (8, 3)?
What type of line does the equation $x + 3y = 6$ represent?
What type of line does the equation $x + 3y = 6$ represent?
What is the equation of the line that passes through the point (4, 2) with a slope of 3?
What is the equation of the line that passes through the point (4, 2) with a slope of 3?
What is the slope of the line that passes through the points (0, 3) and (-5, -3)?
What is the slope of the line that passes through the points (0, 3) and (-5, -3)?
Which equation corresponds to the line that passes through the point (1, -7) with a slope of -1?
Which equation corresponds to the line that passes through the point (1, -7) with a slope of -1?
For the point (-8, 6) and a slope of 4, what is the correct equation of the line?
For the point (-8, 6) and a slope of 4, what is the correct equation of the line?
What equation represents the line with slope -2 passing through the point (9, -4)?
What equation represents the line with slope -2 passing through the point (9, -4)?
How would you express the equation of the line with slope -6 that passes through (6, -6)?
How would you express the equation of the line with slope -6 that passes through (6, -6)?
What is the equation for the line with a slope of 4 that goes through the point (-2, -11)?
What is the equation for the line with a slope of 4 that goes through the point (-2, -11)?
Using the point (-4, 0) and a slope of 2, what is the corresponding equation of the line?
Using the point (-4, 0) and a slope of 2, what is the corresponding equation of the line?
What is the point-slope formula used to write the equation of a line?
What is the point-slope formula used to write the equation of a line?
How would you express the line passing through (4, 1) with a slope of 2 in slope-intercept form?
How would you express the line passing through (4, 1) with a slope of 2 in slope-intercept form?
For which point and slope would the line equation result in a negative slope when written in slope-intercept form?
For which point and slope would the line equation result in a negative slope when written in slope-intercept form?
When applying the point-slope formula, what is the first step after substituting the values?
When applying the point-slope formula, what is the first step after substituting the values?
What is the slope of the line expressed in slope-intercept form from the point (2, 4) with a slope of 1/2?
What is the slope of the line expressed in slope-intercept form from the point (2, 4) with a slope of 1/2?
What will be the y-intercept of the line passing through (-6, -1) with a slope of -1/3?
What will be the y-intercept of the line passing through (-6, -1) with a slope of -1/3?
Which points would result in a horizontal line when using the slope in the point-slope formula?
Which points would result in a horizontal line when using the slope in the point-slope formula?
What is the final form of the line equation for the point (4, -3) and slope -1?
What is the final form of the line equation for the point (4, -3) and slope -1?
What is the reciprocal of -3?
What is the reciprocal of -3?
Which ordered pairs represent segments that are parallel?
Which ordered pairs represent segments that are parallel?
Which equations represent perpendicular lines?
Which equations represent perpendicular lines?
Determine the relationship between AB: (0, -2) to (0, 7) and CD: (3, -5) to (6, -5).
Determine the relationship between AB: (0, -2) to (0, 7) and CD: (3, -5) to (6, -5).
Identify which pairs of lines are neither parallel nor perpendicular.
Identify which pairs of lines are neither parallel nor perpendicular.
Which of the following segments are identified as perpendicular?
Which of the following segments are identified as perpendicular?
What is true about the relationship of the lines represented by y = x and y = -x + 7?
What is true about the relationship of the lines represented by y = x and y = -x + 7?
Choose which of the following segments are parallel.
Choose which of the following segments are parallel.
Which of the following equations represents a line that is parallel to the line given by $y = 3x + 1$?
Which of the following equations represents a line that is parallel to the line given by $y = 3x + 1$?
Identify the equation that represents a line perpendicular to $y = -2x + 6$.
Identify the equation that represents a line perpendicular to $y = -2x + 6$.
Which equation represents a line that is neither parallel nor perpendicular to $y = x + 9$?
Which equation represents a line that is neither parallel nor perpendicular to $y = x + 9$?
Which of the following lines is represented by $5x - 10y = 20$?
Which of the following lines is represented by $5x - 10y = 20$?
Which of the following lines is parallel to the line given by $y = 4x + 9$?
Which of the following lines is parallel to the line given by $y = 4x + 9$?
What is the slope of the line represented by the equation $x - 5y = 30$?
What is the slope of the line represented by the equation $x - 5y = 30$?
Which equation represents a line that is perpendicular to $y = 3x - 7$?
Which equation represents a line that is perpendicular to $y = 3x - 7$?
Determine the type of relationship between the lines represented by $x + y = 7$ and $y = -x + 9$.
Determine the type of relationship between the lines represented by $x + y = 7$ and $y = -x + 9$.
Flashcards
Equation of a Perpendicular Line
Equation of a Perpendicular Line
A line perpendicular to another line has a slope that is the negative reciprocal of the original line's slope.
Slope of a Perpendicular Line
Slope of a Perpendicular Line
The slope of a line perpendicular to a given line is the opposite reciprocal of the given line's slope.
Parallel Lines
Parallel Lines
Parallel lines have the same slope.
Perpendicular Lines
Perpendicular Lines
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Point-Slope Form
Point-Slope Form
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Finding equation of perpendicular line
Finding equation of perpendicular line
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Equation of a line (given point & slope)
Equation of a line (given point & slope)
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Point-slope form
Point-slope form
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Slope
Slope
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Finding Equation of a Line (given point and slope)
Finding Equation of a Line (given point and slope)
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Point-Slope Formula
Point-Slope Formula
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Point-Slope form equation
Point-Slope form equation
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Slope-intercept form
Slope-intercept form
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Finding a line's equation
Finding a line's equation
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Given (x₁, y₁), and slope (m)
Given (x₁, y₁), and slope (m)
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Slope
Slope
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Y-intercept
Y-intercept
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Steps for equation of a line calculation
Steps for equation of a line calculation
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Solve for y
Solve for y
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Parallel Lines
Parallel Lines
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Perpendicular Lines
Perpendicular Lines
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Slope
Slope
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Negative Reciprocal
Negative Reciprocal
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Identifying Parallel Lines
Identifying Parallel Lines
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Identifying Perpendicular Lines
Identifying Perpendicular Lines
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Negative Reciprocals
Negative Reciprocals
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Parallel Lines
Parallel Lines
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Perpendicular Lines
Perpendicular Lines
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Slope of a Line
Slope of a Line
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Determine if Lines are Parallel, Perpendicular, or Neither
Determine if Lines are Parallel, Perpendicular, or Neither
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Finding the slope from coordinates (Two Point Form)
Finding the slope from coordinates (Two Point Form)
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Finding the Equation of a Line (Given a Point and Slope)
Finding the Equation of a Line (Given a Point and Slope)
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(-4, -6) and (3, 8)
(-4, -6) and (3, 8)
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(3, 4) and (-6, -2)
(3, 4) and (-6, -2)
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(-2, -8) and (6, 4)
(-2, -8) and (6, 4)
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(-3, -4); slope = 2
(-3, -4); slope = 2
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(-9, 17); slope = −3/4
(-9, 17); slope = −3/4
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(-4, -5); slope = 4/2
(-4, -5); slope = 4/2
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(-3, 9) and (0, 1)
(-3, 9) and (0, 1)
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(3, 1) and (9, -7)
(3, 1) and (9, -7)
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(3, -7); slope = −8/3
(3, -7); slope = −8/3
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(2, -2) and (8, 1)
(2, -2) and (8, 1)
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(-12, 4) and (0, 2)
(-12, 4) and (0, 2)
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(-6, -4) and (12, 11)
(-6, -4) and (12, 11)
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(6, 6); slope = 5/6
(6, 6); slope = 5/6
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(2, -8); slope = −7/2
(2, -8); slope = −7/2
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(-8, -4) and (4, -7)
(-8, -4) and (4, -7)
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(5, 1) and (10, 5)
(5, 1) and (10, 5)
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(-5, -7); slope = 4/5
(-5, -7); slope = 4/5
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(6, 1); slope = −1/6
(6, 1); slope = −1/6
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(-4, 13) and (-2, 6)
(-4, 13) and (-2, 6)
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(-4, -5); slope = −1/4
(-4, -5); slope = −1/4
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Study Notes
Writing Linear Equations
- Given a point and a slope, use the point-slope formula to find the equation of a line. The formula is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
- Ensure to distribute and solve for y to put the equation in slope-intercept form (y = mx + b).
Writing Linear Equations
- Given two points, use the slope formula (m = (y₂ - y₁)/(x₂ - x₁)) to find the slope between the two points.
- Then, use the point-slope formula (y - y₁ = m(x - x₁)) to find the equation of the line.
- Transform the equation into the slope-intercept form (y = mx + b).
Parallel and Perpendicular Lines
- Parallel lines have the same slope.
- Perpendicular lines have negative reciprocal slopes. The product of their slopes is -1.
Negative Reciprocals
- To find the negative reciprocal of a slope, flip the fraction and change the sign.
Determining if Lines are Parallel or Perpendicular
- If the slopes of two lines are equal, the lines are parallel.
- If the product of the slopes of two lines is -1, the lines are perpendicular.
- If neither of the above conditions is met, the lines are neither parallel nor perpendicular.
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