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We are given two points on the line \(5x - 3y = 15\): \((0, A)\) and \((B, 0)\). We need to find the values of \(A\) and \(B\).

### Step 1: Find \(A\) (where \(x = 0\))

Substitute \(x = 0\) into the line equation:

\[
5(0) - 3y = 15
\]
\[
-3y = 15
\]
\[
y = -5
\]

So, \(A = -5\).

### Step 2: Find \(B\) (where \(y = 0\))

Substitute \(y = 0\) into the line equation:

\[
5x - 3(0) = 15
\]
\[
5x = 15
\]
\[
x = 3
\]

So, \(B = 3\).

### Conclusion:
- \(A = -5\)
- \(B = 3\)

Would you like further details or have any questions?

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Here are 5 related questions for deeper exploration:
1. How can we interpret the meaning of intercepts in a graph?
2. What is the slope of the line \(5x - 3y = 15\)?
3. How would you find the distance between the points \((0, A)\) and \((B, 0)\)?
4. What would happen if the line equation were changed to \(5x + 3y = 15\)?
5. How does changing the coefficients in a linear equation affect the graph?

**Tip:** To find intercepts, substitute 0 for one variable at a time. This helps identify where the line crosses the axes.

The coordinates (0, A) and (B, 0) lie on the line 5x - 3y = 15. What are the values of A and B?

Learn how to find the intercepts A and B for the line 5x - 3y = 15. This algebraic problem involves key concepts like solving for intercepts and understanding linear equations, suitable for students in Grades 8-10.

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