How do I get the equation T=2pi(sqrt(m/k)) to the linear equation y=mx+b?

To convert the equation T=2π√(m/k) into the linear equation form y=mx+b, we need to manipulate the equation to isolate y on one side. Here is the step-by-step process:

Step 1: Start with the equation T = 2π√(m/k).

Step 2: Square both sides of the equation to eliminate the square root:
T^2 = (2π)^2 * (m/k).

Step 3: Simplify the equation:
T^2 = 4π^2(m/k).

Step 4: Multiply both sides of the equation by k to get rid of the fraction:
k * T^2 = 4π^2 * m.

Step 5: Rearrange the equation to isolate m:
m = (k * T^2) / (4π^2).

Step 6: Now, let's rewrite the equation in terms of y instead of m:
y = (k * T^2) / (4π^2).

Step 7: We can see that y is equal to m divided by a constant, so let's denote m as mx, where x is our independent variable.

Step 8: Rewrite the equation as:
y = (k * T^2) / (4π^2) * x.

Step 9: Finally, let's combine the constant terms into a single constant b:
b = (k * T^2) / (4π^2).

Step 10: The resulting equation becomes:
y = mx + b.

Therefore, the linear equation form of T = 2π√(m/k) is y = mx + b, where b = (k * T^2) / (4π^2).