Questions and Answers
What is the equation in slope-intercept form of m=4 and (-1,-6)?
y=4x-2
What is the equation in slope-intercept form of m=2 and (-1,0)?
y=2x+2
What is the equation in slope-intercept form of m=5 and (-2,-3)?
y=5x+7
What is the equation in point-slope form of m=2/5 and (-5,-6)?
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What is the equation in slope-intercept form of m=-1/4 and (4,-3)?
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What is the equation in slope-intercept form of m=-2 and (5,3)?
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What is the equation in slope-intercept form of m=1/2 and (2,6)?
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What is the equation in slope-intercept form of m=1/2 and (2,-3)?
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What is the equation in slope-intercept form of the line passing through the points (1,6) and (2,3)?
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What is the equation in slope-intercept form of the line passing through the points (-1,1) and (1,-1)?
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What is the equation in slope-intercept form of the line passing through the points (5,7) and (3,1)?
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What is the equation in slope-intercept form of the line passing through the points (-6,10) and (-3,-2)?
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What is the equation in slope-intercept form of the line passing through the points (6,6) and (-2,2)?
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What is the equation in slope-intercept form of the line passing through the points (1,4) and (3,18)?
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What is the general slope-intercept form of a line?
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What is the equation of the line in slope-intercept form with a slope of 9 and y-intercept of -2?
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What is the equation in slope-intercept form of the line passing through the points (7,-3) and (2,2)?
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What is the equation of the line in slope-intercept form with a slope of 2 through the point (3,-10)?
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What is the equation in slope-intercept form with m=-3 and b=7?
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What is the equation in slope-intercept form of m=3 and (1,1)?
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What is the equation in slope-intercept form of the line passing through the points (-1,8) and (0,0)?
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What is the equation of the line in slope-intercept form with a slope of 2 and a y-intercept of 3?
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What is the equation of the line in slope-intercept form with a slope of -5 and a y-intercept of 9?
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What is the equation of the line in slope-intercept form with a slope of 1 and a y-intercept of -4?
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What is the equation of the line in slope-intercept form with m=1/2 and b=7?
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What is the equation of the line in slope-intercept form with m=-6 and b=-8?
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What is the equation of the line in slope-intercept form with m=-8 and b=-6?
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What is the equation in slope-intercept form of the line passing through the points (-4,-2) and (4,0)?
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What is the equation in slope-intercept form of m=0 and (0,8)?
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What is the equation in slope-intercept form of m=3 and (1,6)?
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What is the equation in slope-intercept form of m=4 and (2,-3)?
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What is the equation in slope-intercept form of the line passing through the points (7,7) and (-3,7)?
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What is the equation in slope-intercept form of m=-3 and (1,-3)?
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Study Notes
Slope-Intercept Form Overview
- Slope-intercept form is expressed as y = mx + b, where m is the slope and b is the y-intercept.
- A point-slope form can also be transformed into slope-intercept form using coordinates.
Important Examples
- For a slope m = 4 and point (-1, -6), the intercept calculation yields the equation y = 4x - 2.
- A slope of 2 and point (-1, 0 leads to the equation y = 2x + 2.
- Given a slope of 5 and point (-2, -3), the corresponding equation is y = 5x + 7.
Line Equations with Specific Criteria
- y = 2/5x - 4 represents a line with a slope of 2/5 through point (-5, -6).
- A slope of -1/4 passing through (4, -3) results in y = -1/4x - 2.
- From the slope -2 and point (5, 3), the equation is y = -2x + 13.
Applications of Points and Slopes
- For a slope of 1/2 and point (2, 6), the equation appears as y = 1/2x + 5.
- A slope of 1/2 through point (2, -3) leads to y = 1/2x - 4.
- The line through points (1, 6) and (2, 3) can be expressed as y = -3x + 9.
Specific Conditions and Solutions
- The equation of the line between points (-1, 1) and (1, -1) is y = -1x.
- For points (5, 7) and (3, 1), the resulting equation is y = 3x - 8.
- For points (-6, 10) and (-3, -2), the slope-intercept form becomes y = -4x - 14.
Identifying Random Parameters
- Straight lines can have zero or undefined slopes, for example, m = 9 results in y = 9x - 2 or a constant line at y = 8 for m = 0.
- A slope of -1 results in y = -1x + 4 when applied to points (7, -3) and (2, 2).
- The line with slope 2 that passes through (3, -10) is represented as y = 2x - 16.
Summary of Basic Line Properties
- Each line can be identified by its slope and intercept values, allowing classification and graphing.
- The simplest constant function can be identified with a slope of 0, such as y = 7.
Concluding Information
- The operations and calculations shown provide a framework to write equations in slope-intercept form, highlighting relationships between slopes and coordinates to derive the final expressions.
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