Here’s the breakdown of the equations and the table:

Equations:

1. $y = 2x^2 + 4$: This is a quadratic equation. The graph is a parabola that opens upwards, and the constant $4$ shifts the graph upward by 4 units.

2. $y = 4x$: This is a linear equation with a slope of 4. The line passes through the origin.

3. $y = \frac{1}{2}x - 5$: Another linear equation. The slope is $\frac{1}{2}$, and the y-intercept is $-5$.

4. $y = x^2 + 7$: A quadratic equation with a parabola that opens upwards, shifted upward by 7 units.

5. The table: This appears to show a relationship between $x$ and $y$, with $x$ values of $10, 20, 30$ and corresponding $y$ values $1, 2, 3$. This seems to suggest a proportional or linear relationship.

Would you like me to:

1. Solve or analyze any specific equation?
2. Provide graphs for the equations?
3. Interpret the table further?
4. Find if the table corresponds to any of the equations?
5. Explain the relationships in more depth?

Tip: Quadratic equations form parabolas, and their vertex and axis of symmetry are useful for graphing!