Math 103 Section 1.2: Linear Equations and ... - Bruce E. Shapiro

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The graph of an equation y − y 1 = m(x − x 1 ) is a line with slope m passing through the point (x 1 , y 1 ). Example: Find an equation for the line passing through the points (2, 1) and (5, 3). To use the point-slope form for the line, we need to know one point and the slope. In this problem the slope is not given, but two points are known. To find the slope m, we use the fact that m = y 2 − y 1 x 2 − x 1 = So the point-slope form for the equation using (2, 1) as the point is If we use (5, 3) instead, then the point-slope form of the equation is y − 3 = 2 (x − 5). 3 These are two different equations for the same line. 14
Application: Depreciation. Linear Depreciation. Office equipment was purchased for $20,000 and is assumed to have a scrap value of $2,000 after 10 years. If its value is depreciated linearly (for tax purposes) from $20,000 to $2,000: 1. Find the linear equation that relates value (V) in dollars to time (t) in years. (Hint: you know two points.) 15
Page 1 and 2: Math 103 Section 1.2: Linear Equati
Page 3 and 4: x = y x 2 − y = 3 3x − 4y = 6 y
Page 5 and 6: The shape of the graph of a linear
Page 7 and 8: x− and y− intercepts of an equa
Page 9 and 10: Intercepts for the Price-demand equ
Page 11 and 12: Slope of a line: The slope or steep
Page 13 and 14: Special forms for linear equations:
Page 15: Special forms for linear equations:
Page 19 and 20: Application: Linear Interpolation T
Page 21 and 22: Application: Linear Interpolation S

Math 103 Section 1.2: Linear Equations and ... - Bruce E. Shapiro

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