Exercise 9 Page 96

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

We can graph the given data as a scatter plot. Are there 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 Line of Fit

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 (-10,3) and (12,-12) in the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -10,3) & ( 12,-12)

m=-12- 3/12-( -10)

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Simplify

SubNeg

a-(- b)=a+b

m=-12-3/12+10

AddSubTerms

Add and subtract terms

m=-15/22

MoveNegNumToFrac

Put minus sign in front of fraction

m=-15/22

UseCalc

Use a calculator

m=-0.681818...

RoundDec

Round to 1 decimal place(s)

m≈-0.7

Now that we have the slope m≈ -0.7, let's use the point ( -10, 3) 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- 3= -0.7(x-( -10))

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Simplify

SubNeg

a-(- b)=a+b

y-3=-0.7(x+10)

Distr

Distribute -0.7

y-3=-0.7 x -7

AddEqn

LHS+3=RHS+3

y=-0.7 x-4

Note that depending on the trend line that you have drawn, the equation for your line of fit may have a different equation than ours.