Algebra 1 - Slope Flashcards

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.