Meaning of gradient and intercept

[kingstar]

Homework Statement

The velocity of a body traveling in a circular orbit around another body situated at the centre of
the circle, is given by
v = √(GM/r)
where G is the Universal Gravitational constant, M is the mass
of the central body and r is the radius of the orbit. By taking natural logs (ln) of both sides
rearrange the equation in the form of a straight line equation, with r as the independent variable
and identify the meaning of the gradient and the meaning of the intercept

Homework Equations

v = √(GM/r)

The Attempt at a Solution

ln v = (1/2)ln(GM) - (1/2)lnr

y = ln v
x = lnr
c = (1/2)ln(GM)
m = -1/2

I solved the first part but was unsure as to how to answer this part of the question 'identify the meaning of the gradient and the meaning of the intercept'

 

[SammyS]

Homework Statement

The velocity of a body traveling in a circular orbit around another body situated at the centre of
the circle, is given by
v = √(GM/r)
where G is the Universal Gravitational constant, M is the mass
of the central body and r is the radius of the orbit. By taking natural logs (ln) of both sides
rearrange the equation in the form of a straight line equation, with r as the independent variable
and identify the meaning of the gradient and the meaning of the intercept

Homework Equations

v = √(GM/r)

The Attempt at a Solution

ln v = (1/2)ln(GM) - (1/2)lnr

y = ln v
x = lnr
c = (1/2)ln(GM)
m = -1/2

I solved the first part but was unsure as to how to answer this part of the question 'identify the meaning of the gradient and the meaning of the intercept'

For the line, y = mx + b, m is the gradient and of course, b is the intercept.

Rewrite the original equation with rational exponents rather than radicals.