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Questions and Answers
What do the slopes of parallel lines indicate?
What do the slopes of parallel lines indicate?
- The slopes are different
- The slopes are the same (correct)
- The slopes are undefined
- The slopes are opposite reciprocals
What do the slopes of perpendicular lines represent?
What do the slopes of perpendicular lines represent?
- The slopes are different
- The slopes are opposite reciprocals (correct)
- The slopes are zero
- The slopes are the same
What does it mean if the slopes are neither parallel nor perpendicular?
What does it mean if the slopes are neither parallel nor perpendicular?
- The slopes are undefined
- The slopes are the same
- The slopes are opposite reciprocals
- Neither opposite reciprocal nor the same (correct)
How do you graph a line given its equation?
How do you graph a line given its equation?
How to find the equation of a line given two points?
How to find the equation of a line given two points?
How to find the equation of a line given one point and a slope?
How to find the equation of a line given one point and a slope?
How to find the equation of a line given a line parallel and a point?
How to find the equation of a line given a line parallel and a point?
How to find the equation of a line given a line perpendicular and a point?
How to find the equation of a line given a line perpendicular and a point?
How to find the equation of a line given a graph?
How to find the equation of a line given a graph?
How to convert between standard and slope-intercept form and point-slope?
How to convert between standard and slope-intercept form and point-slope?
A horizontal line has a slope of zero.
A horizontal line has a slope of zero.
A vertical line has a slope defined as one.
A vertical line has a slope defined as one.
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Study Notes
Parallel Lines
- Parallel lines have identical slopes, indicating that they run in the same direction.
Perpendicular Lines
- Perpendicular lines have slopes that are opposite reciprocals, meaning if one slope is m, the other is -1/m.
Neither Parallel Nor Perpendicular
- Lines that are neither parallel nor perpendicular have slopes that do not match and are not opposite reciprocals.
Graphing a Line from an Equation
- Begin by plotting the y-intercept on the graph.
- Utilize the slope to find additional points, or create a table to calculate x,y coordinates.
Finding the Equation from Two Points
- Calculate the slope (m) between the two points.
- Substitute the slope into the equation y = mx + b using one point to solve for the y-intercept.
- Alternatively, use the formula y1 - y2 = m(x1 - x2).
Finding the Equation from One Point and Slope
- Insert the known slope and coordinate of the point into the equation format y - y1 = m(x - x1).
Finding the Equation from a Parallel Line and Point
- Use the slope from the parallel line.
- Apply the given point to derive the new line's equation.
Finding the Equation from a Perpendicular Line and Point
- Obtain the opposite reciprocal of the slope from the given perpendicular line.
- Utilize the specified point to formulate the new line's equation.
Finding the Equation from a Graph
- Identify and mark at least two clear points on the graph.
- Determine the slope between those points.
- Choose one point to solve for the y-intercept.
Converting Between Forms
- In standard form, coefficients should be whole numbers and the x coefficient cannot be negative.
- To convert y = mx + b to Ax + By = C, rearrange and adjust constants accordingly.
Horizontal Lines
- A horizontal line has a slope of zero, indicating no vertical change as x changes.
Vertical Lines
- A vertical line has an undefined slope since it cannot be represented as a ratio of vertical change to horizontal change.
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