Question

part a
which of the following graphs represent the proportional relationship described above?
three graphs with axes labeled number of bolts (y) and time (x) or similar, and two categories: graphs that describe the proportional relationship, graphs that do not describe the proportional relationship
part b
what is the constant of proportionality?
blank box for answer

Explanation:

Step1: Define proportional relationship

A proportional relationship has the form $y = kx$ (k is constant), so its graph passes through the origin (0,0) and is a straight line.

Step2: Check each graph

• Left graph: Straight line through (0,0) → proportional.
• Middle graph: Straight line through (0,0) → proportional.
• Right graph: Straight line starts at y>0 (not origin) → non-proportional.

Step3: Identify constant of proportionality

The constant k is the ratio $\frac{y}{x}$ for any (x,y) in the proportional relationship.

Answer:

Graphs that describe the proportional relationship: The Left Graph, The Middle Graph
Graphs that do not describe the proportional relationship: The Right Graph
Constant of proportionality: The ratio of the dependent variable to the independent variable (or $\frac{y}{x}$)