Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
5. Using Linear Models
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Exercise 13 Page 97

Make a scatter plot. Sketch the trend line and write an equation for it.

Example Solution: 6 052 500 tonnes

Practice makes perfect

Let x and y be the production and export, respectively.

Rice Production and Export
Production (1000 tonnes) 15 875 19 225 24 964 32 554 35 600
Export (1000 tonnes) 59 1624 1988 3400 5100

Let's plot the points on the coordinate plane.

Next, we will sketch a trend line to model the scatter plot. Remember that the trend line may vary for each person based where they decided to draw their line of fit.

To write the equation of the line, we should first determine its slope. To do this, we will choose two points on the line. Looking at the graph, we can select the points (20 000,1202) and (30 000,3382). Let's use the Slope Formula!

m = y_2-y_1/x_2-x_1
m = 3382- 1202/30 000- 20 000
m=2180/10 000
m=0.218

Now that we know the slope of the line and a point that it passes through, we can write the equation in the point-slope form. Let (20 000,1202) be our reference point. y-y_1=m(x-x_1) ⇕ [0.5em] y-1202=0.218(x-20 000) Finally, we can substitute 42 250 for x and find how much rice would be exported in 2015.

y-1202=0.218(x-20 000)
y-1202=0.218( 42 250-20 000)
y-1202=0.218*22 250
y-1202=4850.5
y=6052.5
y = 6 052 500

We would expect Vietnam to export 6 052 500 tonnes of rice in 2015.