Question

this equation describes a relationship between x and y. ( y = 2x ) complete the table and select the graph that shows this relationship.
table with columns ( x ) (values: 3, 4, 5, 6) and ( y ) (blank cells)
two coordinate plane graphs (with lines) below the table

Explanation:

Step1: Calculate y when x=3

Given the equation \( y = 2x \), substitute \( x = 3 \) into the equation.
\( y = 2\times3 = 6 \)

Step2: Calculate y when x=4

Substitute \( x = 4 \) into \( y = 2x \).
\( y = 2\times4 = 8 \)

Step3: Calculate y when x=5

Substitute \( x = 5 \) into \( y = 2x \).
\( y = 2\times5 = 10 \)

Step4: Calculate y when x=6

Substitute \( x = 6 \) into \( y = 2x \).
\( y = 2\times6 = 12 \)

For the graph, the equation \( y = 2x \) is a linear equation with a slope of 2 and y - intercept at (0,0). So the graph should pass through the origin (0,0) and have a steeper slope (since slope = 2). Looking at the two graphs, the left - hand graph passes through (0,0) (we can check the points we calculated: (3,6), (4,8), (5,10), (6,12) should lie on the line. The left graph's grid and the slope seem to match this relationship better as the right graph does not pass through the origin (it seems to have a non - zero x - intercept), while \( y = 2x \) has a y - intercept of 0.

Answer:

The completed table is:

x	y
4	8
5	10
6	12

The graph that shows the relationship \( y = 2x \) is the left - hand graph (the one passing through the origin (0,0)).