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Questions and Answers
What is rise over run?
What is rise over run?
slope
What is the slope-intercept form?
What is the slope-intercept form?
y = mx + b
What is the slope formula?
What is the slope formula?
(y₂ - y₁) / (x₂ - x₁)
What is the y-intercept?
What is the y-intercept?
What is standard form?
What is standard form?
Is a horizontal line undefined?
Is a horizontal line undefined?
What is the slope for horizontal lines?
What is the slope for horizontal lines?
Is a vertical line a function?
Is a vertical line a function?
What is the slope of a vertical line?
What is the slope of a vertical line?
The bigger the value of m, the more the slope of the lines ________.
The bigger the value of m, the more the slope of the lines ________.
The smaller the value of m, the more the slope of the lines ________.
The smaller the value of m, the more the slope of the lines ________.
Can you make a perfectly horizontal line?
Can you make a perfectly horizontal line?
Can you make a perfectly vertical line?
Can you make a perfectly vertical line?
How do you find slope?
How do you find slope?
Is y = x a basic linear equation?
Is y = x a basic linear equation?
What is slope?
What is slope?
When graphing an equation, what is the first point you should graph?
When graphing an equation, what is the first point you should graph?
What is the second step when graphing an equation?
What is the second step when graphing an equation?
When finishing up a graph using the y-intercept and rise/run, when connecting the points, make sure your line is...
When finishing up a graph using the y-intercept and rise/run, when connecting the points, make sure your line is...
What is the most basic linear function?
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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