Question

the table represents a linear function.

x	y
-2	-6
0	4
2	14
4	24

what is the slope of the function?
-10
10
5
-5

Explanation:

Step1: Recall slope formula

The slope \( m \) of a linear function 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 points \((-2, -6)\) and \((0, 4)\). Here, \( x_1=-2 \), \( y_1 = -6 \), \( x_2=0 \), \( y_2 = 4 \).

Step3: Calculate the slope

Substitute the values into the slope formula:
\( m=\frac{4 - (-6)}{0 - (-2)}=\frac{4 + 6}{0 + 2}=\frac{10}{2} = 5 \)? Wait, no, wait. Wait, let's check another pair. Let's take \((0,4)\) and \((2,14)\). Then \( x_1 = 0 \), \( y_1=4 \), \( x_2 = 2 \), \( y_2=14 \). Then \( m=\frac{14 - 4}{2 - 0}=\frac{10}{2}=5 \)? Wait, but wait, earlier pair: \((-4,-16)\) and \((-2,-6)\). \( x_1=-4 \), \( y_1=-16 \), \( x_2=-2 \), \( y_2=-6 \). Then \( m=\frac{-6 - (-16)}{-2 - (-4)}=\frac{-6 + 16}{-2 + 4}=\frac{10}{2}=5 \). Wait, but wait the options have 5. Wait, but let's check again. Wait, maybe I made a mistake. Wait, let's take \((-2,-6)\) and \((0,4)\): \( y_2 - y_1 = 4 - (-6)=10 \), \( x_2 - x_1 = 0 - (-2)=2 \), so \( 10/2=5 \). Yes, so the slope is 5. Wait, but wait the options: 5 is an option. Wait, but let me check another pair. \((2,14)\) and \((4,24)\): \( 24 -14=10 \), \( 4 -2=2 \), \( 10/2=5 \). So the slope is 5. Wait, but the options have 5. Wait, but the initial thought: maybe I miscalculated. Wait, no, the formula is correct. So the slope is 5. Wait, but the options: 5 is there. So the answer is 5. Wait, but let me check again. Wait, the table: when x increases by 2 (from -4 to -2, -2 to 0, 0 to 2, 2 to 4), y increases by 10 (from -16 to -6: -6 - (-16)=10; -6 to 4: 4 - (-6)=10; 4 to14:10;14 to24:10). So the change in y is 10, change in x is 2, so slope is 10/2=5. Yes, so slope is 5. So the answer is 5.

Answer:

5