IM Pre-Alg: Unit 4 Vocabulary Quiz

Expressions that are always equal to each other.

• equivalent expressions

• equations

• slope

• constant of proportionality

Answer explanation

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. No matter what value we use for x, these expressions are always equal. When x is 3, both expressions equal 21. When x is 10, both expressions equal 70.

A part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together.

Answer explanation

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. For example, the expression 5x+18 has two terms. The first term is 5x and the second term is 18.

To do this to an expression, you would use the distributive property to rewrite a product as a sum.

• expand

• reduce

• simplify

• retract

Answer explanation

To expand an expression, we use the distributive property to rewrite a product as a sum. The new expression is equivalent to the original expression.

For example, we can expand the expression 5(4x+7) to get the equivalent expression 20x+35.

To do this to an expression, you would use the distributive property to rewrite the sum as a product. You would use a common factor of all terms and then divide all terms by that amount and rewrite the expression.

• factor

• eliminate

• substitute

• simplify

Answer explanation

To factor an expression, we use the distributive property to rewrite a sum as a product. The new expression is equivalent to the original expression.

For example, we can factor the expression 20x+35 to get the equivalent expression 5(4x+7).

A term that does not change value and does not contain a variable.

• constant

• variable

• slope

• rate of change

Answer explanation

In an expression like 5x+2, the number 2 is called the constant term because it doesn't change when x changes.

In the expression 7x+9, 9 is the constant term.

In the expression 5x+(-8), -8 is the constant term.

In the expression 12−4x​​​​​​​, 12 is the constant term.

A number that is multiplied by a variable.

• constant

• variable

• coefficient

• term

Answer explanation

A coefficient is a number that is multiplied by a variable.

For example, 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⋅y.

A set of equations where you want to find a solution that makes all the equations true at the same time.

• system of equations

• linear relationship

• equivalent expressions

• variable

Answer explanation

A system of equations is a set of equations where you want to find a solution that makes all the equations true at the same time.

In these materials it is a pair of two linear equations in two variables.

A system for telling where points are. It has two axes, x and y.

• slope

• coordinate plane

• constant of proportionality

• linear

Answer explanation

The coordinate plane is a system for telling where points are. For example. point R is located at (3,2) on the coordinate plane, because it is three units to the right and two units up.

The point (0,0) in the coordinate plane. This is where the horizontal (x) and vertical (y) axis cross.

Answer explanation

The origin is the point (0,0) in the coordinate plane. This is where the horizontal axis and the vertical axis cross.

The amount y changes when x increases by 1. Also called the slope.

• slope

• linear

• rate of change

• origin

Answer explanation

The rate of change in a linear relationship is the amount y changes when x increases by 1. The rate of change in a linear relationship is also the slope of its graph.

In this graph, y increases by 15 dollars when x increases by 1 hour. The rate of change is 15 dollars per hour.