Unit 6
Glossary
Grade 6
A coefficient is a number that is multiplied by a variable.
- In the expression \(3x+5\), the coefficient of \(x\) is 3.
- In the expression \(y+5\), the coefficient of \(y\) is 1, because \(y=1 \boldcdot y\).
The dependent variable is the result of a calculation.
For example, a boat travels at a constant speed of 25 miles per hour. The equation \(d=25t\) describes the relationship between the boat's distance and time. The dependent variable is the distance traveled because \(d\) is the result of multiplying 25 by \(t\).
A graph of 10 points plotted in the coordinate plane with the origin labeled "O". The horizontal t axis is labeled "time in hours". The numbers 0 through 10, in increments of 2, are indicated, and there are vertical gridlines midway between. The vertical axis is labeled "distance traveled in miles". The numbers 0 through 250, in increments of 25, are indicated, and there are horizontal gridlines midway between. The data are as follows: 1 comma 25. 2 comma 50. 3 comma 75. 4 comma 100. 5 comma 125. 6 comma 150. 7 comma 175. 8 comma 200. 9 comma 225. 10 comma 250.
Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.
For example, \(3x+4x\) is equivalent to \(5x+2x\).
- When \(x\) is 3, both expressions equal 21.
- When \(x\) is 10, both expressions equal 70.
- When \(x\) is any other number, both expressions still have equal value.
The independent variable is used to calculate the value of another variable.
For example, a boat travels at a constant speed of 25 miles per hour. The equation \(d=25t\) describes the relationship between the boat's distance and time. The independent variable is time because \(t\) is multiplied by 25 to get \(d\).
A graph of 10 points plotted in the coordinate plane with the origin labeled "O". The horizontal t axis is labeled "time in hours". The numbers 0 through 10, in increments of 2, are indicated, and there are vertical gridlines midway between. The vertical axis is labeled "distance traveled in miles". The numbers 0 through 250, in increments of 25, are indicated, and there are horizontal gridlines midway between. The data are as follows: 1 comma 25. 2 comma 50. 3 comma 75. 4 comma 100. 5 comma 125. 6 comma 150. 7 comma 175. 8 comma 200. 9 comma 225. 10 comma 250.
A solution to an equation is a number that can be used in place of the variable to make the equation true.
- The solution to the equation \(m+1=8\) is 7, because it is true that \(7+1=8\).
- The solution to \(m+1=8\) is not 9, because \(9+1\) does not equal 8.
A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together.
- 7, \(y\), and \(9a\) are examples of terms.
- The expression \(5x+3\) has 2 terms: \(5x\) and \(3\).
A variable is a letter that represents a number. Different numbers can be chosen for the value of the variable.
In the expression \(10-x\), the variable is \(x\).
- If the value of \(x\) is 3, then \(10-x=7\), because \(10-3=7\).
- If the value of \(x\) is 6, then \(10-x=4\), because \(10-6=4\).