Suppose a relationship is proportional and the point (4, 10) lies on the graph of the proportional relationship. Which of the following points also lies on the graph of the line?

In a proportional relationship, the equation of the line can be written as:

\[
y = kx
\]

where \( k \) is the constant of proportionality, and \( x \) and \( y \) are the coordinates of points on the line.

We know that the point (4, 10) lies on the graph, so we can substitute \( x = 4 \) and \( y = 10 \) into the equation to find \( k \):

\[
10 = k \cdot 4
\]
\[
k = \frac{10}{4} = 2.5
\]

Thus, the equation of the proportional relationship is:

\[
y = 2.5x
\]

Now, we can use this equation to find other points that lie on the line by checking if they satisfy the equation \( y = 2.5x \).

Would you like to provide a list of points to check, or shall I suggest some for you?

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**Relative Questions:**

1. What is a proportional relationship in terms of a graph?
2. How can you find the constant of proportionality from two given points?
3. What is the difference between direct and inverse proportionality?
4. How do proportional relationships compare to linear relationships in general?
5. Can a proportional relationship ever have a y-intercept other than 0?

**Tip:** In any proportional relationship, the ratio \( \frac{y}{x} \) remains constant across all points on the graph.

Explore how to determine other points on the graph of a proportional relationship given the point (4, 10). Using the constant of proportionality and the formula y = kx, learn how to identify additional points that lie on the same line. This problem is ideal for students in Grades 6-8.

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