A linear function is one where the relationship between the variables can be represented by an equation of the form:

$y = mx + b$

where:

• $m$ is the slope (rate of change).
• $b$ is the y-intercept.

Let's analyze the given options:

1. $y = 10x + 2.5$
   This is in the form $y = mx + b$, where $m = 10$ and $b = 2.5$. This is a linear function.

2. $y = 10t^2$
   This equation contains a squared term ($t^2$), which makes it a quadratic function, not linear.

3. $y^2 - 5 = 0$
   This equation involves $y^2$, which is also a non-linear equation (a form of quadratic).

4. $y = x + 2$
   This is also in the form $y = mx + b$, where $m = 1$ and $b = 2$. This is another linear function.

Thus, the linear functions are:

• $y = 10x + 2.5$
• $y = x + 2$

Would you like more details on linear functions or further clarification?

Here are some additional questions for you:

1. How do you identify the slope and y-intercept in a linear function?
2. What is the difference between a linear and quadratic function?
3. Can a linear equation have higher powers of $x$ like $x^2$?
4. How does the graph of a linear function look compared to a quadratic function?
5. What are the real-world examples where linear functions are used?

Tip: When in doubt, check if the equation has variables raised to only the first power (linear), or if they include higher powers (quadratic, cubic, etc.).