Math Problem Statement

What is the constant of proportionality, y/x, based on the given graph showing a proportional relationship between y and x?

Solution

To find the constant of proportionality, yx\frac{y}{x}, we need to choose a point on the graph and calculate the ratio of yy to xx.

From the graph, one clear point is (1,50)(1, 50). At this point:

yx=501=50.\frac{y}{x} = \frac{50}{1} = 50.

Thus, the constant of proportionality is 50.

Would you like further details or help solving similar problems?

Here are 5 follow-up questions related to this topic:

  1. What does the constant of proportionality represent in a real-world context?
  2. How can you verify if a relationship is proportional by looking at a table of values?
  3. What is the equation of a line with a proportional relationship between yy and xx?
  4. How do proportional relationships differ from linear relationships that are not proportional?
  5. How would the graph change if the constant of proportionality were larger or smaller?

Tip: Always check the origin in proportional graphs—it must pass through (0,0)(0, 0) for the relationship to be proportional!

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Math Problem Analysis

Mathematical Concepts

Proportional Relationships
Linear Equations

Formulas

y = kx
k = y/x

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 6-8