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Linear Models & Rates of Change (Precalculus Review 2)

September 6th, 2017. Linear Models & Rates of Change (Precalculus Review 2). I. The Slope of a Line. Def: slope = m = y/ x = (y 2 - y 1 )/(x 2 - x 1 ) *slope of vertical lines is undefined. II. Equations of Lines. Point-Slope Equation of a Line: y - y 1 = m(x - x 1 ).

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Linear Models & Rates of Change (Precalculus Review 2)

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  1. September 6th, 2017 Linear Models & Rates of Change (Precalculus Review 2)

  2. I. The Slope of a Line • Def: • slope = m = y/ x = (y2 - y1)/(x2 - x1) • *slope of vertical lines is undefined

  3. II. Equations of Lines • Point-Slope Equation of a Line: • y - y1 = m(x - x1)

  4. Ex. 1: Find the equation of the line that has a slope of -5 and passes through the point (2, -3).

  5. III. Ratios & Rates of Change The slope of a line on the x- and y-axes that have equal units of measure is a ratio. When the x- and y-axes have different units of measure, the slope can be interpreted as the rate of change.

  6. IV. Graphing Linear Models Slope-Intercept Equation of a Line: y = mx + b slope y-intercept

  7. *Other Equations of Lines: • 1. General Form: Ax + By + C = 0 • 2. Vertical Line: x = a • 3. Horizontal Line: y = b

  8. V. Parallel & Perpendicular Lines Parallel lines have equal slopes (m1 = m2). Perpendicular lines have opposite reciprocal slopes (m1 = -1/m2).

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