What is the angle between the lines y = 3x + 2 and y = -1/3x + 1? (2021)

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Question: What is the angle between the lines y = 3x + 2 and y = -1/3x + 1? (2021)

Options:

Correct Answer: 90 degrees

Exam Year: 2021

Solution:

The slopes are m1 = 3 and m2 = -1/3. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(10/8) = 90 degrees.

What is the angle between the lines y = 3x + 2 and y = -1/3x + 1? (2021)

What is the angle between the lines y = 3x + 2 and y = -1/3x + 1? (2021)

Step 1: Identify the equations of the lines. The first line is y = 3x + 2 and the second line is y = -1/3x + 1.
Step 2: Find the slopes of both lines. For the first line, the slope (m1) is 3. For the second line, the slope (m2) is -1/3.
Step 3: Use the formula to find the angle θ between the two lines: θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|).
Step 4: Calculate m1 - m2: 3 - (-1/3) = 3 + 1/3 = 10/3.
Step 5: Calculate 1 + m1*m2: 1 + (3 * -1/3) = 1 - 1 = 0.
Step 6: Since the denominator is 0, this indicates that the lines are perpendicular.
Step 7: Therefore, the angle θ between the two lines is 90 degrees.

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