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Let's solve the problem for the equation \( y = \frac{2}{3}x + 6 \).

### Finding the x-intercept:
The x-intercept occurs when \( y = 0 \). So, we set \( y = 0 \) in the equation and solve for \( x \):

\[
0 = \frac{2}{3}x + 6
\]

Subtract 6 from both sides:

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

Now, multiply both sides by \( \frac{3}{2} \) to isolate \( x \):

\[
x = -6 \times \frac{3}{2} = -9
\]

So, the x-intercept is \( x = -9 \).

### Finding the y-intercept:
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation:

\[
y = \frac{2}{3}(0) + 6 = 6
\]

So, the y-intercept is \( y = 6 \).

### Final Answer:
- x-intercept: \( -9 \)
- y-intercept: \( 6 \)

Would you like further details or explanations?

Here are five follow-up questions based on this content:
1. How do you calculate the slope of a line from an equation in slope-intercept form?
2. What happens to the intercepts if the slope of the line changes?
3. How do we solve for the intercepts if the equation is not in slope-intercept form?
4. Can you determine intercepts for a vertical or horizontal line?
5. How do intercepts help in graphing a linear equation?

**Tip:** The slope-intercept form, \( y = mx + b \), is useful because the value of \( b \) gives the y-intercept directly!

Find the x-intercept and y-intercept for the equation y = (2/3)x + 6.

Learn how to find the x-intercept and y-intercept for the linear equation y = (2/3)x + 6. This tutorial walks through solving the problem using algebraic methods to find intercepts, which are key for graphing linear equations. Suitable for students in Grades 8-10.

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