 ###### Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

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# Intercepts of Linear Equations - Problem 3

Alissa Fong ###### Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

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At the x-intercept, the coordinate is written as (x, 0), where the value of x is the point that the line crosses the x-axis. At the y-intercept, the coordinate is written as (0, y), where the value of y is the point that the line crosses the y-axis. To interpret what the intercepts mean, look at the variables being compared. At the x-intercept, whatever the y-axis represents is at 0. At the y-intercept, whatever the x axis represents is at 0.

X and y intercepts are really important to word problems having to do with linear equations. This one I got out of an older Math textbook, so we’re going to see what we think of it.
The world population of cheetahs at the turn of the century was 100,000 by 1980 it was reduced to 25,000. Use the graph to predict when cheetahs will become extinct if the current rate of decline continues.
So as of 1980 when this textbook was written, we know that there was only that many cheetahs, and they told us, actually they didn’t tell us, but we’re going to infer that there was a linear rate of decline, meaning they kept declining at the same rate. So we’re going to see if that rate continued, when would cheetahs have become extinct?

Let’s check out the graph. This graph is nice because it’s already done and labeled for us. We have number of cheetahs here, and then here we have years since 1900. So at 1900, at the turn of the century, we have 100,000 cheetahs and then here is the other point we’re given. 80 years later, the population was 25,000. So it asks us, when will cheetahs become extinct. Extinct means that there’s no more left, so I want my y value to be 0. In other words, I’m looking for the x intercept.

Look at the x axis and there it is right there at approximately 109-ish, 108-ish. What that means is 108 years after 1900. If you translate that into a year, that would mean the year 2008, maybe 2009. So we know that cheetahs aren’t really extinct because some people got involved and helped cheetahs retain their population. Had they not gotten involved somewhere after the 1980s and this is just a little piece of the graph, cheetahs would have been extinct already. That’s pretty scary.

So the thing I like about this problem is it shows how sometimes Math books are old and you have to remember that when you’re looking at the word problems, but it also shows at least from this problem how humans were able to intervene and stop what would have been an extinction here at the y intercept, excuse me the x intercept of this graph.