By Bessaih H., Flandoli F.

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Dynamical Systems and Fractals: Computer Graphics Experiments with Pascal

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Extra info for 2-D Euler equation perturbed by noise

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28. 30. 32. ͑12, 0͒, ͑0, Ϫ8͒ ͑2, 4͒, ͑4, Ϫ4͒ ͑Ϫ2, 1͒, ͑Ϫ4, Ϫ5͒ ͑0, Ϫ10͒, ͑Ϫ4, 0͒ Using a Point and Slope In Exercises 35–42, use the point on the line and the slope m of the line to find three additional points through which the line passes. ) ͑2, 1͒, m ϭ 0 36. ͑3, Ϫ2͒, m ϭ 0 ͑Ϫ8, 1͒, m is undefined. ͑1, 5͒, m is undefined. ͑Ϫ5, 4͒, m ϭ 2 ͑0, Ϫ9͒, m ϭ Ϫ2 1 41. ͑Ϫ1, Ϫ6͒, m ϭ Ϫ 2 1 42. ͑7, Ϫ2͒, m ϭ 2 35. 37. 38. 39. 40. y 14. Graphing a Linear Equation In Exercises 15–24, find the slope and y-intercept (if possible) of the equation of the line.

Moreover, because the slope is m ϭ 2, the line rises two units for each unit the line moves to the right. y 5 y = 2x + 1 4 3 m=2 2 (0, 1) x 1 2 3 4 5 When m is positive, the line rises. b. By writing this equation in the form y ϭ ͑0͒x ϩ 2, you can see that the y-intercept is ͑0, 2͒ and the slope is zero. A zero slope implies that the line is horizontal—that is, it does not rise or fall. y 5 4 y=2 3 (0, 2) m=0 1 x 1 2 3 4 5 When m is 0, the line is horizontal. c. By writing this equation in slope-intercept form xϩyϭ2 Write original equation.

1. Rewrite the equation so that y is isolated on the left side. 2. Enter the equation into the graphing utility. 3. Determine a viewing window that shows all important features of the graph. 4. Graph the equation. Intercepts of a Graph y x No x-intercepts; one y-intercept It is often easy to determine the solution points that have zero as either the x-coordinate or the y-coordinate. These points are called intercepts because they are the points at which the graph intersects or touches the x- or y-axis.