Slope fields

[lisafaustina]

Ok I don't get slope fields , is the slope field graph in it's differentiated form or what??

[superflya]

its the graph of the differential equations. the reason why there are so many lines is because when u integrate to get your original equation, there will be an unknown constant.

[kyzoo]

Official definition - the slope field assigns a value (the gradient) to each point on the graph.

Say the slope field is defined by dy/dx = y/x
At (1,1), dy/dx = 1. So you draw a line with gradient +1 at the point (1,1). you repeat this for every other point

When you have all the little dashes marked in, you can see the family of solution curves. Like, if you connect a certain series of dashes, you will get one solution curve (to dy/dx = y/x) - y = f(x). If you connect the series of dashes above that one, you get "y = f(x) + 1."

Hope that isn't too confusing =X

[lisafaustina]

Hmmmm ok so if you have a slope field and if say it's a multiple choice question and you get all these possible equations, do you have to estimate an equation for the graph represented on the slope field and somehow integrate it to find the answer?

[kyzoo]

Hmmmm ok so if you have a slope field and if say it's a multiple choice question and you get all these possible equations, do you have to estimate an equation for the graph represented on the slope field and somehow integrate it to find the answer?

That's one way (Although you differentiate the graph equation represented on the slope field, not integrate it). Another way is to take a single point on the slope field, estimate the value of the gradient of the dash that has been alloccated to it, and then sub the co-ordinates of that point into "dy/dx = ..." Eliminate dy/dx equations one by one.

[superflya]

yea as kyzoo has said go with subbing in points for questions like that and if ur lucky u can find flat dashes on the slope field meaning d/dx=0 at that point.

[Martoman]

Hmmmm ok so if you have a slope field and if say it's a multiple choice question and you get all these possible equations, do you have to estimate an equation for the graph represented on the slope field and somehow integrate it to find the answer?

Slope fields, like art, should be seen holisitcally. Look at the bigger picture. That bigger picture is the graph of the antiderivative.

[itolduso]

disagree

[Martoman]

How?  :coolsmiley:

[itolduso]

the graph of the antiderivative of a continuous function is continuous, not straight line segments

[Martoman]

You miss my point  ...... obviously what you are saying is true yet my explanation is to facilitate understanding.