Finding slope

By :Cassandra Lepsch

The Formula

How do u find a slope????• The slope is defined as

the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is

How to find the slope????

• The slope represents the change in the y coordinates over the change in the x coordinates between two points on a line. In other words, slope = change in y / change in x

Example of a problem• Given that the general

solution to the differential equation

•         y' + y/x2 = 0 • is •         y  =  Ce1/x

• Find the solution to the initial value problem

•        •         y' + y/x2 = 0         y(1)

= 4

Answer

• We just plug in 1 for x and 4 for y into  the general solution

•         4  =  Ce1/1 = Ce• Multiplying both sides

by e-1 gives•         C  =  4e-1 • So that the solution is•         y  =  4e-1e1/x

The arguments• The argument takes on one of various semantically forms:• In the classical form, the arguer suggests that making a move in

a particular direction starts something on a path down a "slippery slope". Having started down the metaphorical slope, it will continue to slide in the same direction (the arguer usually sees the direction as a negative direction, hence the "sliding downwards" metaphor).

• Modern usage includes a logically valid form, in which a minor action causes a significant impact through a long chain of logical relationships. Note that establishing this chain of logical implication (or quantifying the relevant probabilities) makes this form logically valid. The slippery slope argument remains a fallacy if such a chain is not established.

Another example• Example: • You are given the point (4,3) and a slope of 2. Find the equation for this line in

point slope form.• Solution:• Just plug the given values into your point-slope formula above. Your point

(4,3) is in the form of (x1,y1). That means where you see y1, use 3. Where you see x1, use 4. Your slope was given to you, so where you see m, use 2. Pretty simple, huh? Your final result should look like:

• • More Practice:• Your point is (-1,5). The slope is 1/2. Create the equation that describes this

line in point-slope form. Try working it out on your own. The answer is: . If

that's not what you got, re-read the lesson and try again.

Pictures

Pictures

THE END!!!!!!!!! YES