find the rule and complete the table.\nin out\n83 9\n 10\n85 11\n89 15\n93 \n 22

Answer

Explanation:

Step1: Analyze the given pairs

Let's assume the rule is of the form (y = ax + b). Using the pairs ((83,9)) and ((85,11)). First, find the slope (a). The slope formula is (a=\frac{y_2 - y_1}{x_2 - x_1}). Here, (x_1 = 83,y_1 = 9,x_2=85,y_2 = 11). So (a=\frac{11 - 9}{85 - 83}=\frac{2}{2}=1).

Step2: Find the value of (b)

Substitute (a = 1) and the point ((83,9)) into (y=ax + b), we get (9=1\times83 + b). Solving for (b): (b=9 - 83=- 74). So the rule is (y=x - 74).

Step3: Find the missing 'In' value for 'Out' = 10

If (y = 10) and (y=x - 74), then (x=y + 74). Substituting (y = 10), we get (x=10+74 = 84).

Step4: Find the missing 'Out' value for 'In' = 93

If (x = 93) and (y=x - 74), then (y=93-74 = 19).

Step5: Find the missing 'In' value for 'Out' = 22

If (y = 22) and (y=x - 74), then (x=y + 74). Substituting (y = 22), we get (x=22+74 = 96).

Answer:

In	Out
84	10
93	19
96	22