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

x y
3 1
4 2
5 3
6 4

y =
x −

1 answer

To determine the linear equation based on the provided table, we need to find a relationship between \( x \) and \( y \).

From the table:

  • When \( x = 3 \), \( y = 1 \)
  • When \( x = 4 \), \( y = 2 \)
  • When \( x = 5 \), \( y = 3 \)
  • When \( x = 6 \), \( y = 4 \)

We can observe that as \( x \) increases by 1, \( y \) increases by 1. This suggests a linear relationship.

We can generalize this relationship:

  • When \( x = 3 \), \( y = 1 \) can be rewritten as \( 1 = 3 - 2 \).
  • When \( x = 4 \), \( y = 2 \) can be rewritten as \( 2 = 4 - 2 \).
  • When \( x = 5 \), \( y = 3 \) can be rewritten as \( 3 = 5 - 2 \).
  • When \( x = 6 \), \( y = 4 \) can be rewritten as \( 4 = 6 - 2 \).

From this, we can derive the general rule:

\[ y = x - 2 \]

Thus, the missing numbers in the linear equation are:

\[ y = x - 2 \]