what does the ratio of the y-coordinate to the x-coordinate for each pair of points on the graph represent?

The ratio of y-coordinates to x-coordinates would be heartbeats per minute.
You can tell this by looking at each axis. Since the y axis is labelled as heartbeats and the x axis is labeled as minutes, we know dividing the two would give us heartbeats in a minute.
The slope is the ratio of the y-coordinate to the x-coordinate for each pair of points.
A linear function is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the initial value of y.
A linear function with point at the origin is given by:
y = mx
Where m is the slope and the ratio of the y-coordinate to the x-coordinate for each pair of points.
The slope is the ratio of the y-coordinate to the x-coordinate for each pair of points.
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