To linearize a non-linear equation, we need to find a transformation that makes it linear. Let's denote the original variables as x and y, and we'll seek new variables u and v that make the equation linear in terms of v.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
We can rewrite Equation 1 in the form y = mx + b by rearranging terms:
y = 1/x^2
Now, let's define new variables u and v such that u = x and v = 1/y.
The linearized equation in terms of v would then be:
v = mu + b
To find the values of m and b that linearize the equation, we need to express v in terms of u using the definitions we made:
v = 1/y = 1/(1/v) = v
This shows that v is already in the form of a linear equation v = mu + b with m = 1 and b = 0.
Therefore, the values of u and v that work to linearize Equation 1 are u = x and v = 1/y, and the resulting values of m and b are m = 1 and b = 0.