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What is the slope-intercept form of a linear equation, and what do $m$ and $b$ represent?

デッキ「Digital SAT: Comprehensive Practice (Math & Reading-Writing)」の単語カード。

解答

$y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y-intercept $(0, b)$.

解説

Slope is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. Parallel lines share identical slopes ($m_1 = m_2$), while perpendicular lines have negative reciprocal slopes ($m_1 \cdot m_2 = -1$).

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