a line passes through the points in this table.\n| x | y |\n| 25 | -35 |\n| 35 | -43 |\n| 45 | -51 |\n| 55 |…

Explanation:

Step1: Recall slope formula

The slope ( m ) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by ( m=\frac{y_2 - y_1}{x_2 - x_1} ).

Step2: Choose two points

Let's take the first two points ((25, - 35)) and ((35, - 43)). Here, (x_1 = 25), (y_1=-35), (x_2 = 35), (y_2=-43).

Step3: Calculate the slope

Substitute the values into the slope formula: (m=\frac{-43-(-35)}{35 - 25}=\frac{-43 + 35}{10}=\frac{-8}{10}=-\frac{4}{5}) (We can also check with other points, for example, using ((35,-43)) and ((45,-51)): (m=\frac{-51-(-43)}{45 - 35}=\frac{-51 + 43}{10}=\frac{-8}{10}=-\frac{4}{5}), which gives the same result)

Answer:

(-\frac{4}{5})