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The given function is:

\[
y = -3x + 2
\]

We need to find the value of \(x\) when \(y = 8\).

### Step-by-step solution:

1. Substitute \(y = 8\) into the equation:

\[
8 = -3x + 2
\]

2. Subtract 2 from both sides to isolate the term with \(x\):

\[
8 - 2 = -3x
\]

\[
6 = -3x
\]

3. Divide both sides by \(-3\) to solve for \(x\):

\[
x = \frac{6}{-3} = -2
\]

Thus, the value of \(x\) is \(-2\).

Would you like further details or have any questions?

### Related questions:
1. What would the value of \(x\) be if \(y = 5\) for the same equation?
2. How do you graph the function \(y = -3x + 2\)?
3. What is the slope and y-intercept of the equation \(y = -3x + 2\)?
4. How do you check if \(x = -2\) is correct in the original equation?
5. How do you solve for \(x\) if the equation was \(y = 3x + 2\)?

### Tip:
Remember, in linear equations like this, the slope (here \(-3\)) determines how steep the line is, and the y-intercept (here \(2\)) tells you where the line crosses the y-axis.

For the function y = -3x + 2, find the x-value that makes y = 8.

Learn how to solve for x in the linear equation y = -3x + 2 when y is given as 8. This algebra problem covers key concepts, including solving linear equations and understanding the slope-intercept form. Suitable for students in Grades 7-9.

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