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

Question

x y
3 1
4 2
5 3
6 4

y =
x −

Answer 1

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:

$$y=x-2$$