The given equation is $y = \frac{1}{4}x + 7$.

To graph this line, follow these steps:

1. Identify the slope ($\frac{1}{4}$) and the y-intercept ($7$).

   • The slope means that for every 4 units you move to the right, the line goes up 1 unit.
   • The y-intercept is the point where the line crosses the y-axis ($0, 7$).

2. Generate additional points using the slope:

   • From $(0, 7)$, move 4 units to the right ($x = 4$) and 1 unit up ($y = 8$). This gives the point $(4, 8)$.

3. Plot at least two points and draw a straight line through them.

I will plot the graph for you. matplotlib.pyplot as plt import numpy as np

Define the equation y = (1/4)x + 7

x = np.linspace(-20, 20, 400) # Generate x values y = (1/4) * x + 7 # Calculate corresponding y values

Plot the line

plt.figure(figsize=(8, 6)) plt.plot(x, y, label=r"$y = \frac{1}{4}x + 7$", color='blue')

Highlight specific points

plt.scatter([0, 4], [7, 8], color='red', label="Key Points (0,7) & (4,8)")

Add labels and title

plt.axhline(0, color='black',linewidth=0.5) # x-axis plt.axvline(0, color='black',linewidth=0.5) # y-axis plt.grid(color = 'gray', linestyle = '--', linewidth = 0.5) plt.title("Graph of y = (1/4)x + 7") plt.xlabel("x-axis") plt.ylabel("y-axis") plt.legend()

Show the plot

plt.show()Here is the graph of the line $y = \frac{1}{4}x + 7$. The red points $(0, 7)$ and $(4, 8)$ are key points calculated from the slope and intercept.

Would you like further details or calculations?

Here are 5 related questions for practice:

1. How would the graph change if the slope were $-\frac{1}{4}$?
2. What happens to the graph if the y-intercept changes to 10?
3. How would you write the equation if the line passes through $(-4, 6)$?
4. What is the x-intercept of the current line?
5. Can you identify two other points on the line without using the slope?

Tip: Always identify the slope and intercept to quickly sketch a line.