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Demand curves almost always have negative slopes. The Y value being price and the X value being quantity. The higher the price, the more negative the slope. There are very rare conditions where a demand curve could have a positive slope, but its not normally used in business classes.
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Can slope k of a direct variation be positive?
The slope of the graph of a direct variation is always positive.
Is a horizontal slope always positive?
No, never.
When a pair of variables have a positive correlation will the slope in the regression equation always be positive?
Yes
How do you trace a curve in differential calculus?
To trace a curve using differential calculus, you use the fact that the first derivative of the function is the slope of the curve, and the second derivative is the slope of the first derivative. What this means is that the zeros (roots) of the first derivative give the extrema (max or min) or an inflection point of the function. Evaluating the first derivative function at either side of the zero will tell you whether it is a min/max or inflection point (i.e. if the first derivative is negative on the left of the zero and positive on the right, then the curve has a negative slope, then a min, then a positive slope). The second derivative will tell you if the curve is concave up or concave down by evaluating if the second derivative function is positive or negative before and after extrema.
How the slope of a curved line at a point can be found?
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.
