1. An inverse or negative relationship is a mathematical relationship in which one variable, say y, decreases as another, say x, increases. For a linear (straight-line) relation, this can be expressed as y = a-bx, where -b is a constant value less than zero and a is a constant. For example, there is an inverse relationship between education and unemployment — that is, as education increases, the rate of unemployment decreases
Inverse relationships and their counterpart, direct relationships, are widely used in the physical sciences to describe the relationship between two variables in an equation.
In economic graphing, two variables are said to have an inverse relationship if the graph line slopes downward to the right. 2. A relationship that occurs when variable quantities are directly proportional to one another. A linear relationship can be represented on a graph as a STRAIGHT LINE.
Linear relationships always follow the formula:
y=mx+b
where y is the value of the y-coordinate, where my is the slope of the line, where x is the value of the x-coordinate, and b is the y-intercept.
3. Directly Proportional: If one variable changes by a certain factor, the other changes by that same factor. Ex: y = 5x
Using our example formula, if x = 10, y = _______. If x = 20, y = ______. The both increased by ______ times.
If x goes from 3 to 1, then y goes from ______ to ______. yx Always = ______.
4. Inversely Proportional: If one variable is increased by a certain factor, the other is decreased by that factor.
Ex: PV = 20
Using our example formula, if P = 2. V = _____. If P is doubled, what happens to V? _____________________.
If P = 4, V = _____. If P = 1, V = _____. P times V always equals______. 5. Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.
where: * F is the force between the masses, * G is the gravitational constant, * m1 is the first mass, * m2 is the second mass, and * r is the distance between the masses. 