Each graph below shows a relationship between and .

Question

For each graph, determine whether and are proportional.
If and are proportional, fill in the blank with a number.

Graph 1
y123456789101112x1234567891011120
Proportional
is

Not proportional
Graph 2
y123456789101112x1234567891011120
Proportional
is

Not proportional

Answer 1

To determine if the relationships between \( y \) and \( x \) in the given graphs are proportional, we need to assess whether they form a straight line that passes through the origin (0,0). This is indicative of proportional relationships, where \( y = kx \) for some constant \( k \).

1. Graph 1:

   • If the points in Graph 1 form a straight line that passes through the origin (0,0), then \( y \) and \( x \) are proportional.
   • If they do not form a straight line or do not pass through the origin, then they are not proportional.

   Assume that you find that this graph shows a straight line passing through the origin.

   • Conclusion: Proportional
   • The ratio \( \frac{y}{x} \) is constant, so fill in the blank with the value of this ratio.

2. Graph 2:

   • Similar analysis applies here. Check if the points in Graph 2 form a straight line and whether it passes through the origin.
   • If it does, then \( y \) and \( x \) are proportional.
   • If it does not, then they are not proportional.

   Assume that you find that this graph does not pass through the origin.

   • Conclusion: Not proportional

So based on your observations from the graphs, fill out the options accordingly. If you provide specific values or characteristics, I can help you fill in the numbers.