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I am looking a two graphs, the first one is radiation vs $\frac{1}{x^2}$ (Inverse Square Law) and the second one is radiation vs $T^4$(Stefan-Boltzmann Law).

The equations of my inverse square graph is

$$y=412.32x+0.5541$$

and for my Stefan-Boltzmann graph it is

$$y=(2 \times 10^{-11})x+0.204$$

What I am trying to understand is, what does the slope and $y$-intercept of each line represent?

For the inverse square line, would the slope represent the baseline radiation, emitted from our source and the $y$-intercept is our ambient radiation?

For the Stefan-Boltzmann Law, I have seen repeatedly is that there are other equations derived from it, that involve the universal gravitational constant, is that what my slope is representing and the $y$-intercept is our error?

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  • $\begingroup$ what you give as linear equation seams the tangent of the graph at some special point, since it does not give the equation of the laws. Tso this are two different questions. Strange that the slope of the 1/r^2 should be positiv? What is the x in your equation? the slope of the tangent gives you how much the radiation changes at that point approximately if you change distance ( or temperture) by one unit. the y intercept does not say much. $\endgroup$
    – trula
    Commented Sep 22, 2022 at 14:13
  • $\begingroup$ Can you provide the graphs? What is being plotted vs what? $\endgroup$
    – RC_23
    Commented Sep 22, 2022 at 15:19
  • $\begingroup$ @RC_23 I'm trying too but each time i embed the link nothing shows up. $\endgroup$
    – Eric Brown
    Commented Sep 22, 2022 at 15:25
  • $\begingroup$ Please specify clearly what x and y is in both equations. $\endgroup$
    – Karthik
    Commented Sep 23, 2022 at 13:38

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