Question

the table represents a linear function.

x	y
-1	2
0	-4
1	-10
2	-16

what is the slope of the function?

• $-6$
• $-4$
• $4$
• $6$

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through 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 points \((-2, 8)\) and \((-1, 2)\). Here, \( x_1=-2 \), \( y_1 = 8 \), \( x_2=-1 \), \( y_2=2 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{2 - 8}{-1-(-2)}=\frac{-6}{-1 + 2}=\frac{-6}{1}=-6 \)? Wait, no, wait. Wait, let's check another pair. Let's take \((-1,2)\) and \((0, - 4)\). Then \( x_1=-1 \), \( y_1 = 2 \), \( x_2=0 \), \( y_2=-4 \). Then \( m=\frac{-4 - 2}{0-(-1)}=\frac{-6}{1}=-6 \). Wait, but let's check with \((0,-4)\) and \((1,-10)\). \( x_1 = 0\), \( y_1=-4 \), \( x_2 = 1\), \( y_2=-10 \). Then \( m=\frac{-10-(-4)}{1 - 0}=\frac{-6}{1}=-6 \). Wait, but the options have -6 as an option. Wait, but let's check the first calculation again. Wait, when we take \((-2,8)\) and \((-1,2)\): \( y_2 - y_1=2 - 8=-6 \), \( x_2 - x_1=-1-(-2)=-1 + 2 = 1 \). So \( m=\frac{-6}{1}=-6 \). Wait, but let's check the difference in y - values. From \( x=-2 \) to \( x=-1 \), \( y \) changes from 8 to 2, which is a change of \( 2 - 8=-6 \). The change in \( x \) is \( -1-(-2)=1 \). So slope is \( \frac{-6}{1}=-6 \).

Answer:

\(-6\) (corresponding to the option with -6, e.g., if the options are A. -6, B. -4, C. 4, D. 6, then the answer is A. -6)