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!