# Direct Variation Worksheets

How to Spot Direct Variation in Data Sets We know so may quantities that increase at a constituent rate. For example, driving your car at a consistent rate or if you save money weekly, then your savings increase at a consistent rate. If we graph these consistent values, we will get a linear equation. Here we will study the direct variation. In a direct variation, two quantities, like hours and pay, or distance and tie, decrease or increase at a constituent rate. The consistent rate that increases and decreases are known as the constant of variation. One way of spotting direct variation is by data sets. In the table given below, we will study the consistent rate of your weekly savings of \$50. As this is a direct variation, we assume that you start with zero saved money. (Week| Amount) Data = 0, 0 - 1, \$50 - 2, \$100 - 3, \$150 - 4, \$200 - 5, \$250. We can notice two key points about this table: 1. At the start, you have \$0 at week 0. Hence, it is the first entry of the table, and it will be the first entry of any direct variation table. 2. Each week you save \$50, and the amount increases by \$50 at the end of every week. \$50 is also known as the constant of variation as it tells us how much is being saved by the end of every week.

• ### Basic Lesson

Demonstrates the concept of variations and the use of cross multiplication. Practice problems are provided. "x varies directly with y". If x = 5 when y = 15, find y when x = 6. The formula for direct variation is y = kx, where k is the constant of variation.

• ### Intermediate Lesson

Explores the use of data charts that exhibit variation. Practice problems are provided. In the following chart, does one variable vary directly with the other?

• ### Independent Practice 1

Contains 20 Direct Variation problems. Example: If 120 calories in 100 grams of a chocolate. About how many calories were in 150 grams of the chocolate that if the number of calories varies directly with the weight of the chocolate. The answers can be found below.

• ### Independent Practice 2

Features another 20 Direct Variation problems.

• ### Homework Worksheet

Example problems are provided and explained. Example: Write equation which represents: p varies directly with q, if p = 9 when q = 27?

• ### Topic Quiz

10 Direct Variation problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Quote From: Anonymous

"Algebraic symbols are used when you do not know what you are talking about."