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

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The slope of a linear equation: the price-demand equation d = 1720 − .50p If price increases by $1 how much does demand decrease? Does this depend on the starting price? If price increases by $1000 how much does demand decrease? Does this depend on the starting price? Is the decrease in demand always .50 times the increase in price? 8
Slope of a line: The slope or steepness of a straight line is the same between any two points on the line. We can reformulate this property of a line in algebraic terms as follows: For any two points (x 1 , y 1 ), (x 2 , y 2 ) on the line, the ratio of the change in y (change in y is y 2 − y 1 ) to the change in x (x 2 − x 1 ) is the same no matter which two points on the line are chosen. This common ratio is the slope of the line. Definition 3 The slope of a line is defined as m = y 2 − y 1 x 2 − x 1 where (x 1 , y 1 ) and (x 2 , y 2 ) are ANY two points on the line. What is the slope of the line defined by the linear equation 4x − 3y = 12? What is the slope of the line defined by the linear equation d = 1720 − .50p? 9
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: Intercepts for the Price-demand equ
Page 13 and 14: Special forms for linear equations:
Page 15 and 16: Special forms for linear equations:
Page 17 and 18: Application: Depreciation. Linear D
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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