Questions and Answers
What is rise over run?
slope
What is the slope-intercept form?
y = mx + b
What is the slope formula?
(y₂ - y₁) / (x₂ - x₁)
What is the y-intercept?
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What is standard form?
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Is a horizontal line undefined?
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What is the slope for horizontal lines?
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Is a vertical line a function?
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What is the slope of a vertical line?
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The bigger the value of m, the more the slope of the lines ________.
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The smaller the value of m, the more the slope of the lines ________.
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Can you make a perfectly horizontal line?
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Can you make a perfectly vertical line?
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How do you find slope?
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Is y = x a basic linear equation?
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What is slope?
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When graphing an equation, what is the first point you should graph?
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What is the second step when graphing an equation?
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When finishing up a graph using the y-intercept and rise/run, when connecting the points, make sure your line is...
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What is the most basic linear function?
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Study Notes
Slope Concepts
- Rise over Run: The basic definition of slope; measures the vertical change (rise) over the horizontal change (run).
- Slope-Intercept Form: The equation of a line represented as y = mx + b, where m is the slope and b is the y-intercept.
- Slope Formula: Defined mathematically as (y₂ - y₁) / (x₂ - x₁), used to calculate the slope between two points on a graph.
Line Characteristics
- Y-Intercept: The point where a graph intersects the y-axis, represented by the y-coordinate of that point.
- Standard Form: A linear equation expressed as Ax + By = C, where A, B, and C are constants.
- Horizontal Line: Has a slope of 0, indicating no vertical change as the x-value changes; not undefined.
- Vertical Line: Not a function; has an undefined slope due to no horizontal change as the y-value varies.
Graphing Techniques
- Effect of m on Slope: Larger values of m increase the slope's steepness, while smaller values decrease it.
- Perfectly Horizontal Lines: Possible to create, while perfectly vertical lines are not achievable in graphing.
- Finding Slope: Use the formula y₂ - y₁ over x₂ - x₁ to derive slope between two points.
- Basic Linear Equation: An example is y = x, which showcases a constant slope of 1.
Graphing Process
- First Graphing Step: Start by plotting the y-intercept as the initial point.
- Creating Additional Points: Use the rise over run method to establish other points on the graph.
- Connecting Points: Ensure that the line drawn between plotted points is straight for accurate representation of the function.
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Description
Test your knowledge on the concepts of slope with these flashcards. Covering definitions such as rise over run, slope-intercept form, and more, this quiz is perfect for reinforcing your understanding of linear equations. Ideal for students preparing for math exams.
