To find the intercepts of the line given by the equation $5x + 3y - 15 = 0$, follow these steps:

Finding the x-intercept:

The x-intercept occurs where $y = 0$.

Set $y = 0$ in the equation: $5x + 3(0) - 15 = 0$ $5x - 15 = 0$ $5x = 15$ $x = 3$

So, the x-intercept is $(3, 0)$.

Finding the y-intercept:

The y-intercept occurs where $x = 0$.

Set $x = 0$ in the equation: $5(0) + 3y - 15 = 0$ $3y - 15 = 0$ $3y = 15$ $y = 5$

So, the y-intercept is $(0, 5)$.

Drawing the Graph:

To graph the line $5x + 3y - 15 = 0$, plot the intercepts $(3, 0)$ and $(0, 5)$, and draw a straight line through these points.

I'll generate the graph for you.

Do you have any questions or need further details?

Here are 5 questions you might want to ask next:

1. How do you find the slope of a line from its equation?
2. Can you explain how to convert this equation to slope-intercept form?
3. How do you determine the equation of a line given two points?
4. What is the significance of intercepts in graphing lines?
5. How do you find the distance between two points on a coordinate plane?

Tip: When graphing a line, always plot the intercepts first. This provides two easy points that the line will pass through, making it simpler to draw the correct line.