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2.6 Scatter Diagrams

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2.6 Scatter Diagrams

A relation is a correspondence

between two sets

X is the independent variable

Y is the dependent variable

The purpose of a scatter diagram is to show the type of relationship, or correlation that exists between two sets of data.

A positive correlation means that as the value of one set of data increases, the other data will also increase.

A negative correlation means that as the value of one set of data increases, the other data will decrease.

2.7 Variation

Let x and y denote 2 quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number k such that

y = kx

The number k is called the constant of proportionality.

Let x and y denote 2 quantities. Then y varies inversely with x, or y is inversely proportional to x, if there is a nonzero number k such that

y = k / x

When a variable quantity Q is proportional to the product of 2 or more other variables, we say that Q varies jointly with these quantities.

Combinations of direct and / or inverse variation may occur. This is referred to as combined variation.

- a varies directly with b; a = 24 when b = 6
- m varies inversely with n squared; m = 2 and n = 3
- z varies jointly with w and the square root of b; z = 18, w = 4, and b = 9
- m varies directly with the square of b and inversely with the cube root of a; m = 4, b = 3, and a = 27

Express the variation algebraically

Use k for the constant of variation

Find k from the given information

Write the specific formula for the variation

Solve for the required unknown in the problem

Hooke’s Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 12 pounds stretches a certain spring 8 inches, how much will a force of 30 pounds stretch the string?

The illumination produced by a light source varies inversely as the square of the distance from the source. The illumination of a light source at 5 meters is 70 candela. What is the illumination 12 meters from the source?

The weight of an object on Earth is directly proportional to the weight of that same object on the moon. A 200 pound astronaut would weigh 32 pounds on the moon. How much would a 50 pound dog weigh on the moon?