Question

A graph shows an x-axis ranging from 0 to 12 in increments of 2 and a y-axis ranging from 0 to 84 in increments of 14.
Using the points shown in the graph, identify the constant of proportionality for this graph.

Answer 1

To find the constant of proportionality from a graph with the given axes, you typically need to identify points on the graph that represent a direct relationship (proportional relationship) between the two variables represented by the x-axis and the y-axis.

Since the x-axis ranges from 0 to 12 in increments of 2, and the y-axis ranges from 0 to 84 in increments of 14, let's denote the x-values as \( x \) and the y-values as \( y \).

If the graph shows a straight line through the origin (0,0), we can find the constant of proportionality (k) using any point (x, y) on the line, using the formula:

\[
y = kx
\]

This gives us:

\[
k = \frac{y}{x}
\]

Let's say you have two points from the graph, for example:
- Point A: (2, 14)
- Point B: (6, 42)

You can calculate the constant of proportionality (k) with these points:

For Point A (2, 14):

\[
k = \frac{y}{x} = \frac{14}{2} = 7
\]

For Point B (6, 42):

\[
k = \frac{y}{x} = \frac{42}{6} = 7
\]

Assuming that you confirm this with all other points on the graph, the constant of proportionality remains consistent.

Thus, if all points yield the same ratio, the constant of proportionality for the graph is **7**.