Fill in the missing values in the tables given the equations: a) y = 2x − 3, b) a = b + 2, c) m = n * 4

Here are the completed tables based on the given equations:

a) $y = 2x - 3$

• For $x=1$: $y = 2(1) - 3 = 2 - 3 = -1$
• For $x=2$: $y = 2(2) - 3 = 4 - 3 = 1$
• For $x=3$: $y = 2(3) - 3 = 6 - 3 = 3$
• For $x=4$: $y = 2(4) - 3 = 8 - 3 = 5$
• For $x=5$: $y = 2(5) - 3 = 10 - 3 = 7$
• For $x=6$: $y = 2(6) - 3 = 12 - 3 = 9$
• For $x=7$: $y = 2(7) - 3 = 14 - 3 = 11$

The completed table for a) is:

$$\begin{array}{|c|c|} \hline x & y \\ \hline 1 & \boxed{-1} \\ \hline 2 & \boxed{1} \\ \hline 3 & \boxed{3} \\ \hline 4 & \boxed{5} \\ \hline 5 & \boxed{7} \\ \hline 6 & \boxed{9} \\ \hline 7 & \boxed{11} \\ \hline \end{array}$$

b) $a = b + 2$

• For $b=1$: $a = 1 + 2 = 3$
• For $b=2$: $a = 2 + 2 = 4$
• For $b=3$: $a = 3 + 2 = 5$
• For $b=4$: $a = 4 + 2 = 6$

The completed table for b) is:

$$\begin{array}{|c|c|} \hline b & a \\ \hline 1 & \boxed{3} \\ \hline 2 & \boxed{4} \\ \hline 3 & \boxed{5} \\ \hline 4 & \boxed{6} \\ \hline \end{array}$$

c) $m = n \times 4$

• For $n=3$: $m = 3 \times 4 = 12$
• For $n=4$: $m = 4 \times 4 = 16$
• For $n=5$: $m = 5 \times 4 = 20$
• For $n=6$: $m = 6 \times 4 = 24$
• For $n=7$: $m = 7 \times 4 = 28$
• For $n=10$: $m = 10 \times 4 = 40$
• For $n=100$: $m = 100 \times 4 = 400$

The completed table for c) is:

$$\begin{array}{|c|c|} \hline n & m \\ \hline 3 & \boxed{12} \\ \hline 4 & \boxed{16} \\ \hline 5 & \boxed{20} \\ \hline 6 & \boxed{24} \\ \hline 7 & \boxed{28} \\ \hline 10 & \boxed{40} \\ \hline 100 & \boxed{400} \\ \hline \end{array}$$

d) $x = z + 2$

• For $z=2$: $x = 2 + 2 = 4$
• For $z=3$: $x = 3 + 2 = 5$
• For $z=4$: $x = 4 + 2 = 6$
• For $z=5$: $x = 5 + 2 = 7$
• For $z=6$: $x = 6 + 2 = 8$

The completed table for d) is:

$$\begin{array}{|c|c|} \hline z & x \\ \hline 2 & \boxed{4} \\ \hline 3 & \boxed{5} \\ \hline 4 & \boxed{6} \\ \hline 5 & \boxed{7} \\ \hline 6 & \boxed{8} \\ \hline \end{array}$$

e) $m = 3n + 2$

• For $n=1$: $m = 3(1) + 2 = 3 + 2 = 5$
• For $n=5$: $m = 3(5) + 2 = 15 + 2 = 17$
• For $n=10$: $m = 3(10) + 2 = 30 + 2 = 32$
• For $n=20$: $m = 3(20) + 2 = 60 + 2 = 62$
• For $n=25$: $m = 3(25) + 2 = 75 + 2 = 77$

The completed table for e) is:

$$\begin{array}{|c|c|} \hline n & m \\ \hline 1 & \boxed{5} \\ \hline 5 & \boxed{17} \\ \hline 10 & \boxed{32} \\ \hline 20 & \boxed{62} \\ \hline 25 & \boxed{77} \\ \hline \end{array}$$