Select the equations that show a proportional relationship between $$ x $$ and $$ y $$. $$ y=5 x+7 $$ $$ y=8 x $$

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UpStudy AI · Accepted Answer

1. A proportional relationship between $$ x $$ and $$ y $$ has the form
   $$
   y = kx,
   $$
   where $$ k $$ is a constant, and the equation passes through the origin (i.e., when $$ x = 0 $$, then $$ y = 0 $$).

2. The equation
   $$
   y = 5x + 7
   $$
   has a constant term $$ 7 $$. This means it does not pass through the origin, so it does not show a proportional relationship.

3. The equation
   $$
   y = 8x
   $$
   is in the form $$ y = kx $$ (with $$ k = 8 $$) and passes through the origin. Therefore, it represents a proportional relationship.

4. The final answer is:
   $$
   y = 8x.
   $$
The equation $$ y = 8x $$ shows a proportional relationship between $$ x $$ and $$ y $$.

Select the equations that show a proportional relationship between and .

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