Match the graph of each line in (a)–(d) with its slope in...

Match the graph of each line in (a)–(d) with its slope in A–D.
(a)CAN'T COPY THE GRAPH
(b)CAN'T COPY THE GRAPH
(c)CAN'T COPY THE GRAPH
(d)CAN'T COPY THE GRAPH
A. $\frac{2}{3}$
B. $\frac{3}{2}$
C. $-\frac{2}{3}$
D. $-\frac{3}{2}$

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Key Concepts

Slope

The slope of a line in coordinate geometry represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It is a fundamental measure that indicates how steep the line is and in which direction it is inclined.

Positive vs Negative Slope

A positive slope means the line rises from left to right, indicating that as the x-values increase, the y-values also increase. In contrast, a negative slope means the line falls from left to right, so as x increases, y decreases.

Steepness and Absolute Value of the Slope

The absolute value of a slope measures the steepness of the line. A larger absolute value indicates a steeper incline or decline, while a smaller absolute value denotes a gentler slope. This concept allows comparisons between lines regardless of their direction.

Graphical Analysis of Lines

Analyzing the graph of a line involves observing its inclination to determine the slope. By assessing whether the line runs upward or downward and how sharply it does so, one can match the observed line with its numerical slope, linking visual geometry with algebraic representations.

Transcript

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