Which set(s) of points show x in direct proportion to y?
a) {e, c, b} only
b) {g, c, a} only
c) {f, e, d} and {e, c, b} only
d) {f, g, h} and {g, c, a} only

OPTION D.

Step-by-step explanation:

For this exercise it is important to remember that:

1.  Direct proportion equations have the following form:

Where "k" is the constant of proportionality.

2. The graph of Direct proportions is an straight line that passes through the origin.

Observe the picture attached.

If you join the points G, C and A, you get a straight line that passes through the origin,

If you join the points F, G and H, you also get a straight line that passes through the origin,

Therefore, the sets of points show "x" in Direct proportion to "y", are:

and  

correct answers below:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1