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

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

Step 1: Identify the equations of the lines. The first line is y = 2x + 3 and the second line is y = -1/2x + 1.
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 -1/2.
Step 4: Use the formula to find the angle θ between the two lines: θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)|.
Step 5: Substitute the values of m1 and m2 into the formula: θ = tan^(-1) |(2 - (-1/2)) / (1 + 2 * (-1/2))|.
Step 6: Simplify the expression: (2 + 1/2) = 5/2 and (1 - 1) = 0.
Step 7: The formula now looks like θ = tan^(-1) |(5/2) / 0|.
Step 8: Since division by zero is undefined, this indicates that the angle is 90 degrees.
Step 9: Conclude that the angle between the two lines is 90 degrees.

No concepts available.