https://file.aiquickdraw.com/mathbot/file/1727791244845zhe6q92t.jpg

The equation provided from the image is:

\[
\frac{2}{3}x + 4 = y
\]

This represents a linear equation in slope-intercept form \( y = mx + b \), where:
- \( m = \frac{2}{3} \) (the slope),
- \( b = 4 \) (the y-intercept).

### Solving for \( x \) in terms of \( y \):
To solve for \( x \), we can rearrange the equation:

\[
\frac{2}{3}x + 4 = y
\]

Subtract 4 from both sides:

\[
\frac{2}{3}x = y - 4
\]

Now, multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):

\[
x = \frac{3}{2}(y - 4)
\]

Thus, the solution for \( x \) is:

\[
x = \frac{3}{2}(y - 4)
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would you graph this equation on the Cartesian plane?
2. What is the slope and how does it affect the line's steepness?
3. How can this equation be used to model real-world scenarios?
4. What would the equation look like if the slope were different, say \( \frac{3}{2} \) instead of \( \frac{2}{3} \)?
5. How would you interpret the y-intercept in practical terms?

**Tip:** To better understand linear equations, practice transforming them into different forms such as point-slope and standard form!

Learn how to solve the linear equation 2/3x + 4 = y, representing a line in slope-intercept form. This problem explores key algebraic concepts such as slope and y-intercept, suitable for students in Grades 8-10.

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