The equation \( y = 7x - 2 \) represents a linear function. Let's analyze its components:

### Key Features:

1. **Slope (m)**: The coefficient of \( x \) is 7, which means the slope of the line is 7. This tells us that for every 1 unit increase in \( x \), \( y \) will increase by 7 units.
2. **Y-intercept (b)**: The constant term is -2, which means the line crosses the y-axis at \( (0, -2) \).
3. **Graph**: Since the slope is positive, the line will slant upwards from left to right.

### General Form:
The equation is in the **slope-intercept form**:
\[
y = mx + b
\]
where:
- \( m = 7 \) (slope)
- \( b = -2 \) (y-intercept)

### Example:
If you want to find the value of \( y \) for \( x = 3 \), you can substitute:
\[
y = 7(3) - 2 = 21 - 2 = 19
\]
So, when \( x = 3 \), \( y = 19 \).

Would you like more details or have any specific questions?

### Related Questions:
1. How would the graph change if the slope were negative?
2. What are the coordinates of the x-intercept for this line?
3. Can you write the equation in standard form?
4. How do you determine the slope from a graph?
5. What is the significance of the slope and y-intercept in a real-world scenario?

### Tip:
When analyzing linear equations, always look at the slope to understand the rate of change and the y-intercept to know where the line crosses the y-axis.

Understand how to solve the linear equation y = 7x - 2 by identifying its slope (7) and y-intercept (-2). Learn how to graph it and explore the relationship between x and y values. Suitable for Grades 6-8 students.

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