Question

1. does the graph at the right show a proportional relationship between x and y? explain.
2. 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, 10) shows the constant of proportionality.
the constant of proportionality is $\frac{5}{7}$.
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: Recall proportional - relationship criteria

A proportional relationship has a straight - line graph passing through the origin ($(0,0)$) and can be represented by the equation $y = kx$, where $k$ is the constant of proportionality.

Step2: Analyze problem 14

The graph in problem 14 is a curve, not a straight line. For a proportional relationship, the graph must be a straight line passing through the origin. So, the answer to problem 14 is no.

Step3: Analyze problem 15

• For a proportional relationship $y=kx$, if the graph passes through the origin $(0,0)$ and another point $(x,y)$, the constant of proportionality $k=\frac{y}{x}$.
• The graph in problem 15 is a straight line passing through the origin. Let's take the point $(14,10)$. The constant of proportionality $k = \frac{10}{14}=\frac{5}{7}$.
• The point $(1,10)$ is not on the line, so it does not show the constant of proportionality.
• The graph is a straight - line through the origin, so it shows a proportional relationship.
• For the point $(28,20)$, when $x = 28$ (rainfall in cm) and $y = 20$ (plant growth in mm), it means the plant grows 20 mm when it rains 28 cm.

Answer:

1. No. The graph is not a straight line, and for a proportional relationship, the graph must be a straight line passing through the origin.

15.

• The constant of proportionality is $\frac{5}{7}$.
• 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.