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Questions and Answers
What provides the rise over the run?
What is the advantage of the slope-intercept form?
If two lines have slopes m1 and m2, what does it mean if m1 = -1/m2?
What is the standard form of a linear equation?
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What can you do to convert between forms of a linear equation?
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What is the standard form of a linear equation in two variables?
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What does the slope of a line measure?
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How can you find the intercepts of a linear equation?
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What is the formula to calculate the slope of a line?
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What is the graph of a linear equation in two variables?
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What can be said about a line with a zero slope?
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Study Notes
Linear Equations in Two Variables
- A linear equation in two variables is an equation that can be written in the form:
- Ax + By = C
- Where A, B, and C are constants, and A and B are not both zero
- The graph of a linear equation in two variables is a straight line
- The equation can be written in different forms, such as:
- Slope-intercept form (y = mx + b)
- Standard form (Ax + By = C)
Slope of a Line
- The slope of a line is a measure of its steepness
- It is denoted by the letter m and is defined as the ratio of the vertical change (rise) to the horizontal change (run)
- The slope can be calculated using the formula:
- m = (y2 - y1) / (x2 - x1)
- Where (x1, y1) and (x2, y2) are two points on the line
- The slope can be positive, negative, zero, or undefined
- Positive slope: The line slopes upward from left to right
- Negative slope: The line slopes downward from left to right
- Zero slope: The line is horizontal
- Undefined slope: The line is vertical
Graphing Linear Equations
- To graph a linear equation, you can use the following steps:
- Find the intercepts (x-intercept and y-intercept) by setting x or y to 0
- Plot the intercepts on the coordinate plane
- Use the slope to find another point on the line
- Draw the line through the points
- You can also use the slope-intercept form (y = mx + b) to graph the line
- The slope (m) tells you the rise over the run
- The y-intercept (b) tells you the point where the line crosses the y-axis
Forms of the Equation of a Line
- There are several forms of the equation of a line, including:
- Slope-intercept form (y = mx + b)
- Standard form (Ax + By = C)
- Point-slope form (y - y1 = m(x - x1))
- Intercept form (x/a + y/b = 1)
- Each form has its own advantages and disadvantages
- You can convert between forms using algebraic manipulations
Slopes of Parallel and Perpendicular Lines
- Parallel lines have the same slope
- Perpendicular lines have slopes that are negative reciprocals of each other
- If two lines have slopes m1 and m2, then:
- If m1 = m2, the lines are parallel
- If m1 = -1/m2, the lines are perpendicular
- You can use this information to determine whether two lines are parallel or perpendicular
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Description
Learn about linear equations in two variables, including their graph, slope, and different forms. Understand how to graph linear equations and identify parallel and perpendicular lines.
