Find the x- and y-intercepts of the line.
5x + 3y − 15 = 0
x-intercept
(x, y) =

Correct: Your answer is correct.

y-intercept
(x, y) =

Correct: Your answer is correct.

Draw its graph.

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.

![Graph of the line](attachment:graph-of-the-line-5x-3y-15.png)

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.

Learn how to find the x- and y-intercepts of the line given by the equation 5x + 3y − 15 = 0 with a detailed step-by-step solution. This problem covers key concepts in linear equations and graphing lines. Suitable for students in Grades 7-9.

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