Find the angle between the lines y = 2x + 1 and y = -0.5x + 3.
Practice Questions
1 question
Q1
Find the angle between the lines y = 2x + 1 and y = -0.5x + 3.
60 degrees
45 degrees
90 degrees
30 degrees
The slopes are m1 = 2 and m2 = -0.5. The angle θ is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)| = |(2 + 0.5) / (1 - 1)|, which is undefined, indicating 90 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the angle between the lines y = 2x + 1 and y = -0.5x + 3.
Solution: The slopes are m1 = 2 and m2 = -0.5. The angle θ is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)| = |(2 + 0.5) / (1 - 1)|, which is undefined, indicating 90 degrees.
Steps: 8
Step 1: Identify the equations of the lines. The first line is y = 2x + 1 and the second line is y = -0.5x + 3.
Step 2: Find the slope of the first line (m1). The slope is the coefficient of x, which is 2.
Step 3: Find the slope of the second line (m2). The slope is the coefficient of x, which is -0.5.
Step 4: Use the formula to find the angle θ between the two lines: tan(θ) = |(m1 - m2) / (1 + m1*m2)|.
Step 5: Substitute the values of m1 and m2 into the formula: tan(θ) = |(2 - (-0.5)) / (1 + 2 * -0.5)|.
