Question

table 3 (x: 2, 6, 8; y: 1, -1, -2)
table 4 (x: 0, 2, 6; y: 8, 4, -4)
(another table: x: -4, -2, 2; y: 4, 5, 7)
(another table: x: -2, 0, 4; y: 0, 4, 12)
which table describes a linear function that has a slope of 2?
○ table 1
○ table 2
○ table 3
○ table 4

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). We need to calculate the slope for each table using this formula.

Step2: Calculate slope for Table 3 (assuming Table 3 is the bottom - left table with \( x: - 4,-2,2 \) and \( y:4,5,7 \))

Take two points from Table 3, say \((-4,4)\) and \((-2,5)\). Then \( m=\frac{5 - 4}{-2-(-4)}=\frac{1}{2}
eq2 \).

Step3: Calculate slope for Table 4 (top - right table with \( x:0,2,6 \) and \( y:8,4,-4 \))

Take two points \((0,8)\) and \((2,4)\). Then \( m=\frac{4 - 8}{2 - 0}=\frac{-4}{2}=-2
eq2 \).

Step4: Calculate slope for the bottom - right table (Table 4? Wait, the bottom - right table has \( x:-2,0,4 \) and \( y:0,4,12 \))

Take two points \((-2,0)\) and \((0,4)\). Then \( m=\frac{4 - 0}{0-(-2)}=\frac{4}{2} = 2 \). Let's verify with another pair, say \((0,4)\) and \((4,12)\). \( m=\frac{12 - 4}{4 - 0}=\frac{8}{4}=2 \).

Step5: Calculate slope for the top - left table (Table 3 with \( x:2,6,8 \) and \( y:1,-1,-2 \))

Take two points \((2,1)\) and \((6,-1)\). Then \( m=\frac{-1 - 1}{6 - 2}=\frac{-2}{4}=-\frac{1}{2}
eq2 \).

Answer:

Table 4 (the table with \( x:-2,0,4 \) and \( y:0,4,12 \))