Find the x-intercept of the line 9x–3y=24.

To find the x-intercept of the line, we set \( y = 0 \) in the equation \( 9x - 3y = 24 \), since the x-intercept is where the line crosses the x-axis (where \( y = 0 \)).

Starting with the equation:

\[
9x - 3y = 24
\]

Substitute \( y = 0 \):

\[
9x - 3(0) = 24
\]

\[
9x = 24
\]

Now, solve for \( x \):

\[
x = \frac{24}{9} = \frac{8}{3}
\]

Thus, the x-intercept is \( \left( \frac{8}{3}, 0 \right) \).

Would you like a deeper explanation of how this process works, or any other details?

Here are 5 related questions for further practice:
1. Find the y-intercept of the line \( 9x - 3y = 24 \).
2. What is the slope of the line \( 9x - 3y = 24 \)?
3. Write the equation of the line \( 9x - 3y = 24 \) in slope-intercept form.
4. Find the x-intercept of the line \( 7x + 2y = 14 \).
5. Determine the intercepts of the line \( 5x - 4y = 20 \).

**Tip:** The x-intercept occurs when \( y = 0 \), and the y-intercept occurs when \( x = 0 \).

Discover how to find the x-intercept of the line 9x–3y=24 with a detailed solution. This algebra problem explores key concepts such as linear equations and intercepts, ideal for students in Grades 8-10.

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