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On a linear–log plot, pick some fixed point (x 0, F 0), where F 0 is shorthand for F(x 0), somewhere on the straight line in the above graph, and further some other arbitrary point (x 1, F 1) on the same graph. The slope formula of the plot is: = (/) which leads to
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m, a common perpendicular would have slope −1/m and we can take the line with equation y = −x/m as a common perpendicular ...
This is a stylized illustration of the Southern African Great Escarpment, based particularly on its appearance in the Great Karoo, where thick erosion resistant dolerite sills (represented by the thick black lines in the diagram) generally form the upper, sharp edge of the escarpment; in other parts of the escarpment hard erosion-resistant geological layers similarly form the upper, abrupt ...
The second line for angular frequencies above is a line with a slope of −20 dB per decade, since at high frequencies the / term dominates, and the decibel gain expression above simplifies to (/), which is a straight line with a slope of −20 dB per decade. These two lines meet at the corner frequency. From the plot, it can be seen that ...