Question

eight-year-old alex is learning to ride a horse. the trainer says that a horse ages 5 years for every 2 human years. the horse is now 50 years old in human years. is this relationship proportional? why or why not?

no, because it does not pass through the origin
yes, because it is linear
no, because the slope is a fraction
yes, because it has a constant slope

Explanation:

Step1: Recall proportional relationship rule

A proportional relationship between two variables \(x\) and \(y\) follows the form \(y = kx\) where \(k\) is a constant, and its graph must pass through the origin \((0,0)\).

Step2: Analyze the given graph

From the graph, when Alex's age \(x=0\) (human years), the horse's age \(y=30\), not \(0\). The line does not pass through \((0,0)\).

Step3: Evaluate the options

Only the option stating the relationship is not proportional because it does not pass through the origin matches this conclusion.

Answer:

No, because it does not pass through the origin