what is the slope, y int, and x int of the equation: y=1+7x

To analyze the equation \( y = 1 + 7x \), we can identify its slope, y-intercept, and x-intercept.

### 1. Slope
The equation \( y = 1 + 7x \) is in slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

In this case, \( m = 7 \), so the **slope** is \( 7 \).

### 2. Y-intercept
The y-intercept is the point where the graph crosses the y-axis, which occurs when \( x = 0 \).

Substitute \( x = 0 \) into the equation:
\[
y = 1 + 7(0) = 1
\]
Thus, the **y-intercept** is \( (0, 1) \).

### 3. X-intercept
The x-intercept is the point where the graph crosses the x-axis, which occurs when \( y = 0 \).

Set \( y = 0 \) and solve for \( x \):
\[
0 = 1 + 7x
\]
\[
7x = -1
\]
\[
x = -\frac{1}{7}
\]
Thus, the **x-intercept** is \( \left( -\frac{1}{7}, 0 \right) \).

### Summary:
- **Slope**: 7
- **Y-intercept**: \( (0, 1) \)
- **X-intercept**: \( \left( -\frac{1}{7}, 0 \right) \)

Would you like more details or further clarification?

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Here are 5 related questions to expand on this topic:
1. How does the slope of a line affect its steepness?
2. What happens if the slope is negative?
3. Can you find the intercepts for \( y = 2 - 3x \)?
4. How would you graph the equation \( y = 1 + 7x \)?
5. How can you rewrite the equation \( y = 1 + 7x \) in standard form?

**Tip**: When finding intercepts, remember that the x-intercept occurs when \( y = 0 \), and the y-intercept occurs when \( x = 0 \).

Discover how to find the slope, y-intercept, and x-intercept of the linear equation y = 1 + 7x. This detailed step-by-step guide covers essential algebra concepts and is suitable for students in Grades 6-8.

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