positive,negative,zero, or undefined?!
April 26, 2009 6:59pm CST
so i have have homework that says define each slope as a positive,negative,zero, or undefined. i dont really understand how to do that? an example is... y=x+1 can someoen explain how to do that?!
27 Apr 09
Hi there. I wull try my best to explain this. In vector calculus, the slope of a graph or the gradient is a vector field which points in the direction of the greatest rate of increase of the scalar field (the curve of the equation in 3-D). The simplest way to define the gradient of a graph will be apply the del operator on the scalar field and del operator is definite as the sum of partial derivative with respect to x, y and z direction. So, in your example above, the scalar field will be y and the partial derivative of y with respect of x will be 1, and the partial derivative of y with respect to y(not the scalar field y) and z will be 0, so the gradient of the scalar field y is 1 in the x direction. So the slope is positive.
27 Apr 09
Okay, I will try my best :). A line can typically be represented in the following form: y = mx + c, where: y = the vertical axis x = the horizontal axis m = the gradient or the slope of the line. c = a constant - it does not have any effect on the slope of the line, it will just move the line up or down on your plot Here are a few simple examples: a. y = 2x+3. This is a line with a positive slope as m = 2 i.e. m is positive. b. y = -3x+4. This is a line with a negative slope as m = -3 i.e. m is negative. c. y = 3. This can also be written as y = 0x+c. Since m = 0. This is a line with a zero slope. d. x = 3. Notice that there is no y in the equation. In this case you will have a line with undefined slope as the line is a perfectly vertical line. Hopefully my answer above helps. I am unsure if your homework actually cover coordinates (i.e. given two coordinates determine the slope of the line). If you want to discuss this further you can just pm me. P.S. Just in case you are wondering the answer for your original question y = x+1 is a line with a positive gradient as m =1, which is a positive number. L30n84
• United States
27 Apr 09
You just have to figure out what the slope of an equation is. The thing is you have to put in different numbers for x and then graph out the equation. If the line is rising its positive, if the line is falling its negative, is the line is horizontal its zero, etc.