Plot the following coordinates in a graph and draw a straight line that covers all three dots.
(0,4),(1,2),(2,0)

a. What is the y
 value of the line when x=6
 ?
b. What is the y
 value of the line when x=−1
 ?


 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.

Plot the following coordinates in a graph and draw a straight line that covers all three dots. (0,4), (1,2), (2,0)

a. What is the y-value of the line when x=6?
b. What is the y-value of the line when x=−1?

Discover how to plot points (0,4), (1,2), and (2,0) on a graph and derive the linear equation that passes through them. Learn how to calculate slope, y-intercept, and find y-values for given x-values, such as x=6 and x=−1. Ideal for Grades 8-10.

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