Question

the table has two columns. the first column has values -2, -1, 0, 1, 2, 3. the second column has values 8 (for -2), 4 (for -1), 0 (for 0), -4 (for 1), a blank (for 2), and a blank (for 3). we need to find the value for x=2 in the second column.

Explanation:

Step1: Identify the pattern

Looking at the table, when \( x = -2 \), \( y = 8 \); \( x = -1 \), \( y = 4 \); \( x = 0 \), \( y = 0 \); \( x = 1 \), \( y = -4 \). Let's check the relationship between \( x \) and \( y \). For \( x=-2 \), \( y = -4\times(-2)=8 \); \( x = -1 \), \( y=-4\times(-1) = 4 \); \( x = 0 \), \( y=-4\times0=0 \); \( x = 1 \), \( y=-4\times1=-4 \). So the pattern is \( y=-4x \).

Step2: Calculate \( y \) when \( x = 2 \)

Using the formula \( y=-4x \), substitute \( x = 2 \) into it. Then \( y=-4\times2=-8 \).

Answer:

\(-8\)