Exercise 2 Page 340

A trend line is a line drawn through the center of the points on a scatter plot. It shows a correlation between data. To write the equation of a trend line, we should first plot the given points, then sketch a trend line that models the data.

Observing the Graph

By treating the table as a set of points, we can graph the given data as a scatter plot. Do you see any trends?

It looks like there is some kind of correlation. Let's draw a line of fit, or trend line. To do so, we will draw a line that appears to fit the data closely.

Equation for the Trend Line

To write an equation for the line of fit we determined above, we first need to use two points on the line to find its slope. Let's use (25,76) and (40,37) in the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 25,76) & ( 40,37)

m=37- 76/40- 25

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Simplify

SubTerms

Subtract terms

m=-39/15

MoveNegNumToFrac

Put minus sign in front of fraction

m=-39/15

ReduceFrac

a/b=.a /3./.b /3.

m=-13/5

Now, that we have the slope m= - 135, let's use the point ( 25, 76) in the point-slope form to write and simplify an equation for our line of fit.

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y- 76= -13/5(x- 25)

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Simplify

Distr

Distribute -13/5

y-76=-13/5x-(-13/5* 25)

MoveRightFacToNum

a/c* b = a* b/c

y-76=-13/5x-(-13* 25/5)

SubNeg

a-(- b)=a+b

y-76=-13/5x+13* 25/5

ReduceFrac

a/b=.a /5./.b /5.

y-76=-13/5x+13* 5/1

DivByOne

a/1=a

y-76=-13/5x+13* 5

Multiply

Multiply

y-76=-13/5x+65

AddEqn

LHS+76=RHS+76

y=-13/5x+141