matplotlib.pyplot as plt

Coordinates

points = [(0, 4), (1, 2), (2, 0)]

Extract x and y values

x_values, y_values = zip(*points)

Calculate the slope (m) and intercept (b) of the line y = mx + b

m = (y_values[1] - y_values[0]) / (x_values[1] - x_values[0]) b = y_values[0] - m * x_values[0]

Define the line function

def line_function(x): return m * x + b

Generate x values for the line

x_line = range(-1, 7) # From x=-1 to x=6 y_line = [line_function(x) for x in x_line]

Plot the points and the line

plt.figure(figsize=(8, 6)) plt.plot(x_line, y_line, label=f'Line: y = {m:.2f}x + {b:.2f}', color='blue') plt.scatter(x_values, y_values, color='red', label='Points') plt.title('Graph of Points and Line') plt.xlabel('x') plt.ylabel('y') plt.axhline(0, color='black', linewidth=0.5, linestyle='--') plt.axvline(0, color='black', linewidth=0.5, linestyle='--') plt.grid(color='gray', linestyle='--', linewidth=0.5) plt.legend() plt.show()

Compute y values for x=6 and x=-1

y_at_6 = line_function(6) y_at_neg_1 = line_function(-1)

y_at_6, y_at_neg_1a. The y-value of the line when $x = 6$ is $-8.0$.
b. The y-value of the line when $x = -1$ is $6.0$.

Would you like a detailed explanation of the calculations or have further questions?

Here are 5 related questions for exploration:

1. How is the slope of a line calculated from two points?
2. What does the y-intercept represent in a linear equation?
3. How would the line equation change if an additional point was added?
4. Can you verify the equation $y = mx + b$ with other x-values?
5. How does changing the range of x-values affect the graph?

Tip: Always double-check calculations for slope and intercept, as they form the basis for the linear equation.