Question

c circle the tables that show an additive pattern (y = x + a).

Explanation:

Step1: Analyze the first table

For \(x = 2,y=3\), if \(y=x + a\), then \(3=2 + a\), \(a = 1\). Check \(x = 4,y=5\), \(5=4 + 1\); \(x = 6,y=7\), \(7=6 + 1\); \(x = 8,y=9\), \(9=8 + 1\). This table follows \(y=x + 1\).

Step2: Analyze the second table

For \(x = 1,y=7\), if \(y=x + a\), \(a=6\). But \(x = 2,y = 14\), \(14
eq2 + 6\). This is a multiplicative pattern (\(y = 7x\)) not \(y=x + a\).

Step3: Analyze the third table (partial \(x\) values shown, assume full - table analysis)

For \(x = 5,y\) (if full - table), but from the pattern of \(x\) increasing by \(5\), if \(y=x + a\), for \(x = 5\), \(y=5 + a\); \(x = 10\), \(y=10 + a\) etc. But comparing with the fourth table (shown fully), we focus on complete tables.

Step4: Analyze the fourth table

For \(x = 0,y=5\), if \(y=x + a\), \(a = 5\). Check \(x = 1,y=6\), \(6=1 + 5\); \(x = 2,y=7\), \(7=2 + 5\); \(x = 3,y=8\), \(8=3 + 5\). This table follows \(y=x + 5\).

Step5: Analyze the fifth table

For \(x = 4,y=8\), if \(y=x + a\), \(a = 4\). But \(x = 8,y=16\), \(16
eq8 + 4\). This is a multiplicative pattern (\(y = 2x\)) not \(y=x + a\).

Step6: Analyze the sixth table

For \(x = 3,y\) (if full - table), \(x\) increases by \(3\). For \(x = 3,y\) (assuming \(y=x + a\)), \(y=3 + a\); \(x = 6,y=6 + a\) etc. But comparing with complete tables, the first and fourth tables are complete and follow \(y=x + a\).

Answer:

The first and fourth tables (the one with \(x = 2,y = 3;x = 4,y = 5;x = 6,y = 7;x = 8,y = 9\) and the one with \(x = 0,y = 5;x = 1,y = 6;x = 2,y = 7;x = 3,y = 8\)) should be circled.