Question

the ______ variable is often denoted by x and represents the input or cause in the relationship.

the mathematical concept formed by setting two algebraic expressions equal to each other is called a(n) ______.

the standard form of a linear equation is ( ax + by = c ), where ( a ), ( b ), and ( c ) are ______.

the type of relationship where a constant change in one variable results in a constant change in another variable is called a ______ relationship.

a(n) ______ is a symbol used to represent an unknown value in an equation.

the process of finding the value of a variable that makes an equation true is called ______.

a mathematical expression representing a relationship where one variable is a constant multiple of another is called a ______ equation.

a linear equation with one variable generally takes the form ( ax + b = 0 ), where ( a ) and ( b ) are ______.

Explanation:

1. The input/cause variable in a relationship is the independent variable, often denoted by \(x\).
2. Setting two algebraic expressions equal forms an equation.
3. In \(Ax + By = C\), \(A\), \(B\), and \(C\) are fixed values (constants).
4. A relationship with constant changes in both variables is linear.
5. A symbol for an unknown in an equation is a variable.
6. Finding the variable value making an equation true is solving the equation.
7. A variable as a constant multiple of another is direct variation.
8. In \(ax + b = 0\), \(a\) and \(b\) are fixed values (constants).

Answer:

1. independent
2. equation
3. constants
4. linear
5. variable
6. solving the equation
7. direct variation
8. constants