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Explanation:
Pick any two points from the table to find the slope. I'll use the first two rows.
Let [tex](x_1,y_1) = (-4,-11) \text{ and } (x_2,y_2) = (-2,-6)[/tex]
So the slope is...
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-6 - (-11)}{-2 - (-4)}\\\\m = \frac{-6 + 11}{-2 + 4}\\\\m = \frac{5}{2}\\\\[/tex]
This means the answer is between choices A and D.
If we plugged in the set of x,y values from row 2, into the point-slope formula, then we would have
[tex]y - y_1 = m(x - x_1)\\\\y - (-6) = \frac{5}{2}(x - (-2))\\\\y + 6 = \frac{5}{2}(x +2)\\\\[/tex]
which leads to choice D as the answer.
