Questions and Answers
What is a coordinate plane?
What is the horizontal axis called?
x-axis
What is the vertical axis called?
y-axis
What do ordered pairs represent?
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What is the first coordinate in an ordered pair called?
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What is the second coordinate in an ordered pair called?
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What is the point where the x and y axes cross called?
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What is the definition of a slope?
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What is the formula for slope?
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What does a positive slope indicate?
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What does a negative slope indicate?
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What type of line has an undefined slope?
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What type of line has a zero slope?
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What is the y-intercept?
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What is the x-intercept?
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What is the structure of the slope-intercept form?
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The Origin is represented by the coordinates ______
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What does the 'Three Musketeer Rule' refer to in graphing?
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What do the terms Domain and Range refer to?
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Match the following terms with their definitions:
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In inequalities, when do I use a dashed line? ______
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What should you do with a non-integer result in slope?
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Study Notes
Coordinate Plane
- Consists of two intersecting axes: the horizontal x-axis and the vertical y-axis.
Ordered Pairs
- A format to represent a point on the graph, structured as (x,y).
Coordinates
- X-coordinate: The first value in an ordered pair, indicating horizontal position.
- Y-coordinate: The second value in an ordered pair, indicating vertical position.
Origin and Quadrants
- Origin is the point where the x-axis and y-axis cross, represented as (0,0).
- The coordinate plane is divided into four quadrants based on the sign of the coordinates.
Slope Concepts
- Slope (m) measures the steepness of a line.
- Positive slope: Line rises from left to right.
- Negative slope: Line falls from left to right.
- Undefined slope: A vertical line where x-coordinates are constant.
- Zero slope: A horizontal line where y-coordinates are constant.
Formulas
- Slope formula: m = (y2 - y1) / (x2 - x1) = rise/run.
- Slope-Intercept Form: Expresses a line as y = mx + b, where m is the slope and b is the y-intercept.
- Standard Form: Ax + By = C, which can be analyzed using the cover-up method.
Intercepts
- Y-intercept: The point where the line crosses the y-axis.
- X-intercept: The point where the line crosses the x-axis.
Graphing Techniques
- Cover-Up Method: Used to graph intercepts directly from standard form equations.
Inequalities
- Dashed line is used when the inequality is strict (< or >), indicating the line is not included.
- Solid line is used when the inequality is inclusive (≤ or ≥), indicating the line is included.
Special Rules
- HOY (Horizontal, Zero Slope, y = # equation) simplifies understanding horizontal lines.
- VUX (Vertical, Undefined Slope, x = # equation) simplifies understanding vertical lines.
Other Concepts
- Domain refers to the set of possible y-values for a function.
- Range refers to the set of possible x-values for a function.
- For non-integer results, rewrite in Slope-Intercept form for ease of use.
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Test your understanding of key concepts related to the slope in Algebra 1 through this flashcard quiz. Each card features essential vocabulary and definitions that will help reinforce your knowledge of coordinate planes and ordered pairs.