Why Graph? Graphs tell a story (and help answer questions)!

Please brainstorm Why did we graph the volume and mass to get density? Why didn’t we just measure one volume and one mass, do the division, and call it “good”?

Why not just one point? Our measurements are not exact, we could have made a mistake or not been careful enough. That means we wouldn’t be sure if we were getting the most trustworthy density.

Why a graph? With a graph it is easier to see outliers. We want a general relationship over a wider range of situations. That general relationship helps us build a mathematical model.

Slope vs. Averages If we just averaged the points…we would do one calculation and then lose the information (it becomes a fact instead of a tool). A graph gives us an equation (a mathematical model), a tool we can use again and again. A graph can be used to predict volumes or masses you didn’t measure.

Speaking of predicting… A couple of vocab words: – Extrapolate: use the graph to predict values outside the range of data points – Interpolate: use the graph to predict values inside the range, but not the actual data points

Slope Slope = rise = Δ mass = mass run Δvolume volume Slope = Density! So… Volume (mL) Mass (g) y = mx + b