Subjects algebra

Slope Ordering

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1. **Problem Statement:** Arrange the given slope values $3$, $\frac{4}{5}$, $-4$, $-\frac{11}{2}$, $1.5$, and $0$ in order from least steep to most steep. 2. **Understanding Slope:** The slope of a line measures its steepness and direction. A positive slope means the line rises as it moves from left to right, a negative slope means it falls, and zero slope means the line is horizontal. 3. **Convert all slopes to decimal for easy comparison:** - $3$ stays $3$ - $\frac{4}{5} = 0.8$ - $-4$ stays $-4$ - $-\frac{11}{2} = -5.5$ - $1.5$ stays $1.5$ - $0$ stays $0$ 4. **Order the slopes from least to greatest:** - $-5.5$ (steepest negative) - $-4$ - $0$ - $0.8$ - $1.5$ - $3$ (steepest positive) 5. **Final ordered sequence from least steep to most steep:** $$-\frac{11}{2}, -4, 0, \frac{4}{5}, 1.5, 3$$ This sequence arranges the slopes from the most negative (steepest downward) to the most positive (steepest upward).