Question

Fill in the missing numbers to complete the linear equation that gives the rule for

this table.
11
1
2
3
4
x +
y
9
10
11
12

Answer 1

The missing numbers are x+8y−1.

To find the rule for the given table, let's analyze the relationship between the values of x and y.

Looking at the given table:

1:9

2:10

3:11

4:12

We can observe that y is increasing by 1 for every increase of 1 in x. Additionally, when x=1, y is 9, and this suggests a starting value of 8 for y. Therefore, the rule for the table can be expressed as x+8y−1.

This rule is consistent with the values in the table:

1+8(9)−1=1+72−1=72

2+8(10)−1=2+80−1=81

3+8(11)−1=3+88−1=90

4+8(12)−1=4+96−1=99

So, the complete linear equation that gives the rule for this table is x+8y−1.