y = sin (x - 2)
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The roots of the quadratic equation are the x-intercepts of the curve.
y=ax+b
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
The values of many curves cannot be calculated analytically: the process requires painstaking numerical estimation. The values of a standard curve can be calculated once and published for ready reference. This means that, given any other curve in the same family, it is possible to transform it to the standard curve and the reference values can be used.
The coordinates of the points on the curve represent solutions of the equation.