what are the x- and y- intercepts for the  equation 3x+8y=5?

To find the **x-intercept** and **y-intercept** of the equation \(3x + 8y = 5\), we proceed as follows:

### 1. Finding the **x-intercept**:
The x-intercept occurs when \(y = 0\). Substituting \(y = 0\) into the equation:

\[
3x + 8(0) = 5 \quad \Rightarrow \quad 3x = 5 \quad \Rightarrow \quad x = \frac{5}{3}
\]

So, the **x-intercept** is \(\left(\frac{5}{3}, 0\right)\).

### 2. Finding the **y-intercept**:
The y-intercept occurs when \(x = 0\). Substituting \(x = 0\) into the equation:

\[
3(0) + 8y = 5 \quad \Rightarrow \quad 8y = 5 \quad \Rightarrow \quad y = \frac{5}{8}
\]

So, the **y-intercept** is \(\left(0, \frac{5}{8}\right)\).

### Summary:
- **x-intercept**: \(\left(\frac{5}{3}, 0\right)\)
- **y-intercept**: \(\left(0, \frac{5}{8}\right)\)

Would you like more details on any part of this?

### Relative Questions:
1. How do you find intercepts for non-linear equations?
2. What is the slope of the line for the equation \(3x + 8y = 5\)?
3. How can you graph this equation using the intercepts?
4. What does it mean if a line has no intercepts?
5. How would you find intercepts for an equation in slope-intercept form?

**Tip:** When solving for intercepts, always substitute the opposite variable to zero (i.e., \(x = 0\) for y-intercepts and \(y = 0\) for x-intercepts).

what are the x- and y- intercepts for the equation 3x+8y=5?

Learn how to find the x- and y-intercepts of the linear equation 3x + 8y = 5. This guide walks through solving for both intercepts using basic algebra concepts, suitable for students in Grades 7-10.

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