Each graph below shows a relationship between and .

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

Graph 1
y12345678910x123456789100
Proportional
is

Not proportional
Graph 2
y12345678910x123456789100
Proportional
is

Not proportional
Graph 3
y12345678910x123456789100
Proportional
is

Not proportional

1 answer

To determine whether the variables \( y \) and \( x \) are proportional in the graphs you mentioned, we check if the ratio \( \frac{y}{x} \) is constant for all points on the graph.

  1. Graph 1:

    • If the graph is a straight line passing through the origin (0, 0), then \( y \) and \( x \) are proportional.
    • If you find specific points and see they follow a constant ratio, you can determine \( k \) where \( y = kx \).
    • If not, then they are not proportional.
  2. Graph 2:

    • Check the same way as for Graph 1.
    • Look for linearity through the origin.
  3. Graph 3:

    • Again, apply the same reasoning.

Example Analysis:

If all three graphs are proportional with the values being as follows for each:

  • For Graph 1: Suppose the ratio \( \frac{y}{x} \) is 2 when calculating from points, then:

    • Proportional: \( k \) is \( 2 \).
  • For Graph 2: If the ratio \( \frac{y}{x} \) is 3, then:

    • Proportional: \( k \) is \( 3 \).
  • For Graph 3: If the graph indicates that it does not pass through the origin or the ratio is inconsistent:

    • Not Proportional.

To accurately fill in those fields, observe the graphs and use the points to confirm the relationships and compute the ratios. If they yield a constant ratio, state it as \( k \); otherwise, indicate they are not proportional.

Feel free to provide specific points from the graphs if you need further assistance in calculations or ratios!