Select all tables that represent a proportional relationship between x and y. X0 1 2. 3
y 0 9 | 18 27
X 0 3 6 9
y 0 21 42 63
x0 18 16 124
y 1 17 33 49
XO 5 10 | 15
y 2 17 32 47
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Options (1) and (2)

Step-by-step explanation:

Let the proportional relation between x and y is represented by,

y ∝ x

y = kx

Here, k = Proportionality constant

Option 1,

From the given table,

Graph of the points given in the table passes through origin.

For x = 0, y = 0.

For x = 1 and y = 9,

k =

k = 9

For x = 2 and y = 18,

k =

k = 9

Therefore, table represents a proportional relation.

Option 2.

From the given table,

Graph of the points given in the table passes through origin.

For x = 3 and y = 21,

k =

k = 7

For x = 6 and y = 42,

k =

k = 7

Therefore, table represents a proportional relation.

Option 3.

From the given table,

For x = 0, y = 1

But for the proportional relation graph should pass through origin (0, 0).

Therefore, table doesn't represent a proportional relation.

Option 4.

From the table given,

For x = 0, y = 2

Graph of the line doesn't pass through the origin (0, 0)

Therefore, table doesn't represent a proportional relation.  

Options (1) and (2) are the correct options.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.