Determine whether the function is linear or nonlinear. If linear, determine the equation that defines $y=f(x)$. $$ \begin{array}{|rr|} \hline {\boldsymbol{x}} & \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \\ \hline-6 & -3 \\ -3 & -4 \\ 0 & -5 \\ 3 & -6 \\ 6 & -7 \\ \hline \end{array} $$

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So we have a set of data and we want to determine whether we have linear exponential or neither. And let me quick right these values down. And hopefully you see the trend. You know, just pattern wise, you can see that As the X. variable goes up by three, The wife of aerial drops by one. And this is why which is F. A. Back. So we know that the slope between these two points, if this is linear as we take the difference in the wise negative four minus negative three. Over the difference in the axis negative three minus negative six. And when we do that, We find out that this slope is negative 1/3 and notice what happens here. The difference in the wise. Mhm over the difference in the access. This too Is equal to negative 1/3 and that's consistent for all of these pairs. So this is linear and we know that the slope Is -1 3rd. But we also know that the y intercept is negative five. So there is our money, our model. And you can check it by plugging in some points to verify

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