Without graphing, tell whether the slope of a line that...

Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.

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Key Concepts

Slope

Slope is a measure of the steepness and direction of a line, representing how much the dependent variable changes for a unit change in the independent variable. It tells us whether the line rises or falls as we move from left to right and is defined as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run).

Rate of Change in Linear Relationships

In the context of linear relationships, the slope is also known as the rate of change. This represents the constant rate at which one variable changes with respect to another. A positive rate of change indicates that the dependent variable increases as the independent variable increases, while a negative rate of change indicates a decrease. Zero indicates no change, and an undefined rate occurs when there is no horizontal change.

Two-Point Formula

The two-point formula is a method used to calculate the slope of a line by taking any two points on the line. By subtracting the y-coordinates and the x-coordinates of these points and then dividing the former by the latter, we obtain the slope. This formula is fundamental in analyzing linear relationships without needing to visualize their graphs.

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