The convex combination of two points $x$ and $y$ in one dimension is given by:

$z = t \cdot x + (1 - t) \cdot y$

where $t$ is a parameter that lies in the interval $[0, 1]$.

Given $x = 2$, $y = 3$, and $z = 2.75$, we need to find the value of $t$ such that:

$2.75 = t \cdot 2 + (1 - t) \cdot 3$

Let's solve for $t$:

$2.75 = 2t + 3 - 3t$

$2.75 = -t + 3$

$-t = 2.75 - 3$

$-t = -0.25$

$t = 0.25$

Thus, the value of $t$ that makes the convex combination equal to 2.75 is $t = 0.25$.

Would you like further details or have any questions? Here are some related questions you might explore:

1. What happens if $t = 0$ or $t = 1$ in a convex combination?
2. How does the value of $t$ affect the position of $z$ between $x$ and $y$?
3. Can the convex combination be used to represent points in higher dimensions?
4. What is the significance of the interval $[0, 1]$ for $t$ in a convex combination?
5. How would the problem change if $x$ and $y$ were negative?

Tip: In a convex combination, $t$ represents the "weight" given to each point, and varying $t$ moves the result along the line segment between the points $x$ and $y$.