The equation you've provided is in slope-intercept form, \( y = mx + b \), where:

- \( m \) is the slope of the line,
- \( b \) is the y-intercept.

For the equation \( y = -4x - 3 \):

- The slope (\( m \)) is \(-4\).
- The y-intercept (\( b \)) is \(-3\).

### Interpretation:

1. **Slope**: A slope of \(-4\) means that for every unit increase in \( x \), the value of \( y \) decreases by 4 units. The line is descending from left to right.
  
2. **Y-intercept**: The y-intercept is the point where the line crosses the y-axis. Here, it crosses the y-axis at \(-3\) (i.e., at the point \( (0, -3) \)).

### Graphing the Line:

- Start at the y-intercept, \( (0, -3) \).
- From this point, use the slope to determine the direction of the line. Since the slope is \(-4\), move one unit to the right (positive direction on the x-axis) and 4 units down (negative direction on the y-axis).
- Connect these points to form the line.

Would you like more details or have any questions?

### Relative Questions:

1. How do you find the x-intercept of the line \( y = -4x - 3 \)?
2. What would happen to the line if the slope were changed to \( 4 \) instead of \(-4\)?
3. How would the graph change if the y-intercept was \( 3 \) instead of \(-3\)?
4. Can you determine the equation of a line parallel to \( y = -4x - 3 \) that passes through the point \( (1, 2) \)?
5. What are the coordinates of another point on the line, besides \( (0, -3) \)?

### Tip:
When graphing a linear equation, always identify the slope and y-intercept first. This makes it easier to sketch the graph accurately.

Explore the equation y = -4x - 3 in depth with explanations on its slope, y-intercept, and how to graph it. Learn how changes in slope and y-intercept affect the line. Suitable for students in Grades 7-9 studying linear equations and graphing.

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