Grade 8 Functions Progression pg 6

[dsekreta]

A group of Grade 8 teachers were discussing the meaning/interpretation of the narrative on page 6 of the Functions progression document that says, “a linear function does not have a slope but the graph of a non-vertical line has a slope.” The discussion between the teachers was around linear functions versus linear equations and slope in those two concepts. Could you please clarify what the authors of this statement might have meant by this statement so I can share the response(s) with the group of teachers?

[Bill McCallum]

Slope is a geometric concept; it is a property of a line in a coordinate plane. So, a line can have slope. But a function is not a geometric object, so it can’t really have a slope. When people talk about the slope of a linear function, they really mean the slope of its graph, a geometric object which is attached to the function. And if the linear function relates quantities with units, for example distance versus time, then makes more sense to talk about the rate of change rather than the slope.

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