Question

1. the graph at the right shows the relationship between rainfall during the growing season and the growth of a type of plant. which statements about the graph are true?

the point (1, 50) shows the constant of proportionality.
the constant of proportionality is 5/7.
the graph does not show a proportional relationship.
the graph is a straight line through the origin.
the point (28, 20) means the type of plant grows 20 mm when it rains 28 cm.

Explanation:

Step1: Determine if it's a proportional relationship

A proportional relationship graph is a straight - line through the origin. The given graph is a straight - line through the origin, so it shows a proportional relationship.

Step2: Calculate the constant of proportionality

The constant of proportionality \(k=\frac{y}{x}\). For the point \((28,20)\), \(k = \frac{20}{28}=\frac{5}{7}\). For the point \((1,y)\), if \(x = 1\) and \(k=\frac{5}{7}\), then \(y=\frac{5}{7}
eq50\).

Step3: Analyze the meaning of the point \((28,20)\)

In the context of the graph, \(x\) represents rainfall (in cm) and \(y\) represents plant growth (in mm). So the point \((28,20)\) means the plant grows \(20\) mm when it rains \(28\) cm.

Answer:

The graph is a straight line through the origin. The point \((28,20)\) means the type of plant grows \(20\) mm when it rains \(28\) cm.