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Questions and Answers
What is the formula to calculate the slope of a line?
What is the formula to calculate the slope of a line?
What does the 'm' represent in the slope-intercept form of a linear equation?
What does the 'm' represent in the slope-intercept form of a linear equation?
How do you graph a horizontal line?
How do you graph a horizontal line?
What is the standard form of a linear equation?
What is the standard form of a linear equation?
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What is the relationship between the slopes of parallel lines?
What is the relationship between the slopes of parallel lines?
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What is the point-slope form of a linear equation used for?
What is the point-slope form of a linear equation used for?
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Study Notes
Slope of a Line
- The slope of a line can be calculated using the formula: (y2 - y1) / (x2 - x1)
- The slope is a measure of how steep a line is
Slope-Intercept Form
- The slope-intercept form of a linear equation is: y = mx + b
- m represents the slope and b represents the y-intercept
- Example: y = 2x - 3, where m = 2 and b = -3
Graphing Lines
- To graph a vertical line, the equation is x = a, where a is a constant
- To graph a horizontal line, the equation is y = b, where b is a constant
- Example: Graphing x = 2 and y = 3
Slope-Intercept Method
- To graph a line using the slope-intercept method, start with the y-intercept and use the slope to find another point on the line
- Example: Graphing y = 3x - 2
Standard Form
- The standard form of a linear equation is: ax + by = c
- Example: 2x - 3y = 6
- To graph a line in standard form, find the x and y-intercepts
Point-Slope Form
- The point-slope form of a linear equation is: y - y1 = m(x - x1)
- Example: Find the equation of the line passing through the point (2, 5) with a slope of 3
- Convert point-slope form to slope-intercept form by distributing the slope and adding/subtracting terms to both sides
Parallel and Perpendicular Lines
- Parallel lines have the same slope
- Perpendicular lines have slopes that are negative reciprocals of each other
- Example: Find the equation of the line passing through the point (3, -2) and parallel to the line 2x + 5y - 3
- Example: Find the equation of the line passing through the point (-4, -3) and perpendicular to the line 3x - 4y + 5
Slope of a Line
- Calculated using the formula: (y2 - y1) / (x2 - x1)
- Measured by how steep a line is
Slope-Intercept Form
- Equation: y = mx + b
- m represents the slope and b represents the y-intercept
- Example: y = 2x - 3, where m = 2 and b = -3
Graphing Lines
- Vertical line equation: x = a, where a is a constant
- Horizontal line equation: y = b, where b is a constant
- Example: x = 2 and y = 3
Slope-Intercept Method
- Start with the y-intercept and use the slope to find another point on the line
- Example: y = 3x - 2
Standard Form
- Equation: ax + by = c
- Example: 2x - 3y = 6
- Graph by finding x and y-intercepts
Point-Slope Form
- Equation: y - y1 = m(x - x1)
- Example: Find the equation of the line passing through (2, 5) with a slope of 3
- Convert to slope-intercept form by distributing the slope and adding/subtracting terms to both sides
Parallel and Perpendicular Lines
- Parallel lines have the same slope
- Perpendicular lines have slopes that are negative reciprocals of each other
- Example: Find the equation of the line passing through (3, -2) and parallel to 2x + 5y - 3
- Example: Find the equation of the line passing through (-4, -3) and perpendicular to 3x - 4y + 5
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Description
Learn about the slope of a line, its calculation, and its representation in slope-intercept form. Also, discover how to graph vertical and horizontal lines.
