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

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Do you think that all such linear equations, when graphed will give a straight line? Why? Let’s try some examples: 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 10 What about x − y = 0? What about x = 3? What about y = −1? 2
The shape of the graph of a linear equation: Theorem 1 The graph of any equation of the form Ax+By = C is a line, <strong>and</strong> any line in the cartesian coordinate system is the graph of an equation of this form. This theorem makes it very easy to graph a linear equation... For example if we know two points on the graph we are done!! Moral: Theorems are your friends. Two special cases: • Horizontal lines ⇔ y = c for some number c • Vertical lines ⇔ x = c for some number c 3
Page 1 and 2: Math 103 Section 1.2: Linear Equati
Page 3: x = y x 2 − y = 3 3x − 4y = 6 y
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 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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