Questions: 8. x 1 2 3 4 5 y 33 34 35 36 37 9. m 0 1 2 3 4 n 0 3 6 9 12

Solution Steps

• Observe the relationship between \( x \) and \( y \) in the table: \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline y & 33 & 34 & 35 & 36 & 37 \\ \hline \end{array} \]
• Notice that as \( x \) increases by 1, \( y \) increases by 1. This suggests a linear relationship.

• Calculate the slope (\( m \)) using two points from the table, e.g., \( (1, 33) \) and \( (2, 34) \): \[ m = \frac{34 - 33}{2 - 1} = 1 \]
• Use the slope-intercept form \( y = mx + b \) and substitute \( m = 1 \) and one point \( (1, 33) \): \[ 33 = 1(1) + b \implies b = 32 \]
• The equation representing the pattern is: \[ y = x + 32 \]

• Observe the relationship between \( m \) and \( n \) in the table: \[ \begin{array}{|c|c|c|c|c|c|} \hline m & 0 & 1 & 2 & 3 & 4 \\ \hline n & 0 & 3 & 6 & 9 & 12 \\ \hline \end{array} \]
• Notice that as \( m \) increases by 1, \( n \) increases by 3. This suggests a linear relationship.

• Calculate the slope (\( m \)) using two points from the table, e.g., \( (0, 0) \) and \( (1, 3) \): \[ m = \frac{3 - 0}{1 - 0} = 3 \]
• Use the slope-intercept form \( n = mm + b \) and substitute \( m = 3 \) and one point \( (0, 0) \): \[ 0 = 3(0) + b \implies b = 0 \]
• The equation representing the pattern is: \[ n = 3m \]

Final Answer