Question

this equation describes a relationship between x and y.
y = x - 1
complete the table and select the graph that shows this relationship.
(table with x values 1, 2, 3, 4 and empty y cells, followed by two graphs)

Explanation:

Step1: Calculate y for x=1

Substitute $x=1$ into $y=x-1$:
$y=1-1=0$

Step2: Calculate y for x=2

Substitute $x=2$ into $y=x-1$:
$y=2-1=1$

Step3: Calculate y for x=3

Substitute $x=3$ into $y=x-1$:
$y=3-1=2$

Step4: Calculate y for x=4

Substitute $x=4$ into $y=x-1$:
$y=4-1=3$

Step5: Match to correct graph

The equation $y=x-1$ has a y-intercept of $-1$ (when $x=0$, $y=-1$, and the line passes through $(1,0)$, $(2,1)$ etc.), which matches the left graph.

Answer:

Completed table:

x	y
2	1
3	2
4	3

Correct graph: The left graph (passing through (1,0), (2,1), etc.)