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?

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.