https://file.aiquickdraw.com/mathbot/file/1726196499484xqxfocsp.jpg

From the image, I can see that the problem is asking you to verify whether certain points are solutions to linear equations. The task involves plugging the given \(x\) and \(y\) values into the equation and determining if the equation holds true.

Let's break down the two cases visible in the image:

### First Problem:
Check if the point \((3, 5)\) is a solution to the equation \(y = 2x - 1\).
- Plug in \(x = 3\) and \(y = 5\) into the equation:
  \[
  y = 2(3) - 1 = 6 - 1 = 5
  \]
  Since both sides are equal, \((3, 5)\) **is** a solution to the equation \(y = 2x - 1\).

### Second Problem:
Check if the point \((-2, -8)\) is a solution to the equation \(y = 4x + 2\).
- Plug in \(x = -2\) and \(y = -8\) into the equation:
  \[
  y = 4(-2) + 2 = -8 + 2 = -6
  \]
  Since \(-8 \neq -6\), \((-2, -8)\) **is not** a solution to the equation \(y = 4x + 2\).

If you'd like further details on any of these problems or explanations, feel free to ask!

### Related Questions:
1. How can you generalize the process for checking solutions to any linear equation?
2. What are the conditions for a point to lie on the graph of a linear equation?
3. Can you explain what the slope represents in each of these equations?
4. What does it mean geometrically when a point is a solution to an equation?
5. How would the solution process change if we had a system of equations?

### Tip:
When verifying solutions for equations, always substitute both the \(x\) and \(y\) values into the equation and simplify step-by-step to avoid mistakes.

Verify if the points (3,5) and (-2,-8) are solutions to the equations y = 2x - 1 and y = 4x + 2 respectively.

This page provides a detailed guide on how to verify if given points are solutions to specific linear equations, such as y = 2x - 1 and y = 4x + 2. It is suited for high school students learning about linear equations and how to validate solutions mathematically.

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