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# 2.6 Scatter Diagrams PowerPoint PPT Presentation

2.6 Scatter Diagrams. 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. Correlation.

2.6 Scatter Diagrams

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2.6 Scatter Diagrams

### 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.

### Correlation

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

### Direct 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.

### Inverse Variation

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

### Joint Variation andCombined Variation

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.

### Write a general formula to describe each 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

### Solving Variation Problems

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

### Write a general formula and solve each variation 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?

### Write a general formula and solve each variation problem

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?

### Write a general formula and solve each variation problem

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?