Question

1. find the slope of the line that passes through all of the points on the table.

x	y
2	1
5	-5
8	-11
11	-17

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Explanation:

Step1: Recall the 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 from the table

Let's take the first two points \( (2, 1) \) and \( (5, -5) \). Here, \( x_1 = 2 \), \( y_1 = 1 \), \( x_2 = 5 \), \( y_2=-5 \).

Step3: Calculate the slope

Substitute the values into the slope formula:
\( m=\frac{-5 - 1}{5 - 2}=\frac{-6}{3}=-2 \).

We can verify with another pair of points, say \( (5, -5) \) and \( (8, -11) \). Then \( x_1 = 5 \), \( y_1=-5 \), \( x_2 = 8 \), \( y_2=-11 \).
\( m=\frac{-11-(-5)}{8 - 5}=\frac{-6}{3}=-2 \).
Another verification with \( (8, -11) \) and \( (11, -17) \): \( x_1 = 8 \), \( y_1=-11 \), \( x_2 = 11 \), \( y_2=-17 \).
\( m=\frac{-17-(-11)}{11 - 8}=\frac{-6}{3}=-2 \).

Answer:

\(-2\)