Algebraic vocabulary — variables, constants, coefficients, terms

A constant is a fixed number that does not change, no matter what value the variable takes.

In $6x+9$, the term $6x$ contains a variable ($x$) with a coefficient ($6$). The term $9$ is just a number — it has no variable attached to it.

Since $9$ is a standalone number that never changes, $9$ is the constant.

We need to find the constant — a fixed number that has no variable.

The number $6$ is in front of the variable $x$, which makes it a coefficient, not a constant. Eliminate this option.

$x$ is a variable — it represents a changing value. It is not a constant. Eliminate this option.

$6x$ is a variable term — it changes depending on the value of $x$. It is not a constant. Eliminate this option.

The only remaining option, $9$, is a standalone number that never changes. It is the constant.

A coefficient is the number placed in front of a variable. It tells you how many of that variable you have.

In the term $13y$, the number $13$ is written before the letter $y$.

The coefficient of $y$ in $13y$ is $13$.

We are looking for the coefficient — the number multiplying the variable in the term.

$y$ is the variable, not the coefficient. Coefficients are numbers, not letters. Eliminate this option.

A coefficient of $1$ applies when a variable stands alone (e.g. just $y$ with no number in front). Here, $13y$ clearly has $13$ written in front. Eliminate $1$.

$13y$ is the entire term, not just the coefficient. The coefficient is only the numerical part. Eliminate this option.

$13$ is the number in front of $y$, making it the coefficient.