"Which of these best models the data?"

One of my students came up with a slick way to do these. It may seem obvious, but I had not thought of approaching these problems this way, so I thought I would share.

I am talking about the kind where you have a scatter plot and they expect you to choose the equation of the line of best fit. I had always done these by drawing my own line, getting its intercept and slope, and then ruling out any answer choice that was way wrong on either intercept or slope.

While that works every time, my student did something lazier, less math-y, more sneaky:

Pick some x value. Read the approximate y value off the graph. Put that same x value into the answers and rule out any answer that is clearly far from the value you got from the graph. Sometimes, that rules out all but one. But if it doesn’t, repeat the process with another x value.

If the first way seems better to you, stick with it. But as an SAT teacher (and a physics teacher) I know that finding a slope from a graph gives some students a good bit of trouble. My student’s method gets the right answer without ever finding the slope.

As long as that point isn’t an outlier, I guess.

Personally, I would prefer the first method, or as a check, plotting all the points into my calculator and determining line of best fit.