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The slope field of =, with the blue, red, and turquoise lines being +, , and , respectively. A slope field (also called a direction field [ 1 ] ) is a graphical representation of the solutions to a first-order differential equation [ 2 ] of a scalar function.
Three integral curves for the slope field corresponding to the differential equation dy / dx = x 2 − x − 2. If the differential equation is represented as a vector field or slope field, then the corresponding integral curves are tangent to the field at each point.
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let ( m , n ) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point ( x 0 , y 0 ).
Fig. 1: Isoclines (blue), slope field (black), and some solution curves (red) of y' = xy.The solution curves are = /.. Given a family of curves, assumed to be differentiable, an isocline for that family is formed by the set of points at which some member of the family attains a given slope.
The equation ′ = is autonomous, since the independent variable does not explicitly appear in the equation. To plot the slope field and isocline for this equation, one can use the following code in GNU Octave/MATLAB
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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.
SPOILER ALERT: This story discusses major plot points, including the ending for “Gladiator II,” currently playing in theaters. All hail Macrinus! In a world of political backstabbing, power ...