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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

5. Using Linear Models

Finish the assignment

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Exercise 9 Page 96

Can you draw a trend line? If so, which direction does it point as you move from left to right on the graph?

Example Solution: -0.7x-4

Practice makes perfect

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)

▼

Simplify

a-(- b)=a+b

m=-12-3/12+10

Add and subtract terms

m=-15/22

MoveNegNumToFrac

Put minus sign in front of fraction

m=-15/22

Use a calculator

m=-0.681818...

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))

▼

Simplify

a-(- b)=a+b

y-3=-0.7(x+10)

Distribute -0.7

y-3=-0.7 x -7

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.

Subchapter links

Lesson Check p.96

Practice and Problem-Solving Exercises p.96-98

Standardized Test Prep p.98

Mixed Review p.98