Graph 
\[y = -7+4x\].
\[x\]
\[y\]
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To graph the equation \(y = -7 + 4x\), let's follow these steps:

1. **Identify the slope and intercept**:
   - The equation is in the slope-intercept form \(y = mx + b\), where:
     - \(m = 4\) (the slope)
     - \(b = -7\) (the y-intercept)
   - This means the graph crosses the y-axis at \((0, -7)\), and for each unit increase in \(x\), \(y\) increases by 4.

2. **Plot the y-intercept**:
   - Start by plotting the point \((0, -7)\) on the graph.

3. **Use the slope to find another point**:
   - From \((0, -7)\), apply the slope \(m = 4\). This means you move 1 unit to the right (increasing \(x\) by 1), and 4 units up (increasing \(y\) by 4).
   - This gives the point \((1, -3)\).

4. **Draw the line**:
   - Plot more points by continuing to apply the slope or reverse direction (1 unit left, 4 units down).
   - Draw a straight line through the points you have plotted, extending it in both directions.

### Graphing key points:
- Points on the graph: \((0, -7)\), \((1, -3)\), \((2, 1)\), and so on.
- The slope of 4 ensures that for each increase of 1 in \(x\), \(y\) increases by 4.

Would you like a more detailed graph or specific points? Let me know if you need clarification or more information.

### Related Questions:
1. How would the graph change if the slope was negative?
2. What happens if you add or subtract a constant from the equation?
3. Can you find the x-intercept of this line?
4. What would the equation look like if the slope was \( \frac{1}{2} \) instead?
5. How do you interpret the slope and intercept in a real-world context?

**Tip**: Always double-check your slope and intercept values before plotting; they're key to sketching the correct line!

Learn how to graph the linear equation y = -7 + 4x. This problem covers key algebraic concepts, including identifying the slope and intercept, plotting points, and drawing the graph. Suitable for students in Grades 8-10.

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