Find the x- and y-intercepts of the line.
y = 6x + 4


To find the intercepts of the line represented by the equation \( y = 6x + 4 \), we proceed as follows:

### 1. **Finding the y-intercept:**
The y-intercept occurs when \( x = 0 \). To find it, substitute \( x = 0 \) into the equation:

\[
y = 6(0) + 4 = 4
\]

Thus, the **y-intercept** is \( (0, 4) \).

### 2. **Finding the x-intercept:**
The x-intercept occurs when \( y = 0 \). To find it, substitute \( y = 0 \) into the equation and solve for \( x \):

\[
0 = 6x + 4
\]
\[
6x = -4
\]
\[
x = -\frac{4}{6} = -\frac{2}{3}
\]

Thus, the **x-intercept** is \( \left(-\frac{2}{3}, 0\right) \).

### Summary:
- **x-intercept:** \( \left(-\frac{2}{3}, 0\right) \)
- **y-intercept:** \( (0, 4) \)

Would you like a detailed explanation on any of the steps?

Here are 5 related questions to explore further:
1. How do you find the slope of a line given its equation?
2. What is the meaning of the intercepts in the context of real-world problems?
3. How can you graph the line given its equation?
4. What is the difference between the x- and y-intercepts?
5. How do you find intercepts when the equation is in standard form?

**Tip:** The slope of a line gives you the rate at which \( y \) changes for a unit change in \( x \). In \( y = 6x + 4 \), the slope is 6, meaning for each increase of 1 unit in \( x \), \( y \) increases by 6 units.

Find the x- and y-intercepts of the line.
 y = 6x + 4

Learn how to find the x- and y-intercepts of the linear equation y = 6x + 4 using simple algebraic methods. This solution explains how to calculate the intercepts, suitable for students in Grades 8-10.

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