Question

a line passes through the points in this table.

x	y
25	-35
35	-43
45	-51
55	-59

what is the slope of the line?
write your answer as an integer or simplified fraction.

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:

\(-\frac{4}{5}\)