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Big Ideas Math Algebra 1, 2015

BI

Big Ideas Math Algebra 1, 2015 View details

1. Writing Equations in Slope-Intercept Form

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Exercise 29 Page 180

Practice makes perfect

a We are asked to write a linear model that represents the world record (in minutes) for the men's mile as a function of the number of years since 1960. To create this model we will use the world records in 1960 and in 1980.

Year	World Record (minutes)
1960	3.91
1980	3.81

To write the linear model we will use the slope-intercept form of a line, where m is the slope and b is the y-intercept.

y= mx+ b We will let x represent the time in years since 1960 and let y represent the record for the men's mile in minutes. In the model, 1960 corresponds to x=0 and 1980 to x=20.

Year	x	y
1960	0	3.91
1980	20	3.81

The y-intercept is the function's value when x=0. We have that point from the given data. Let's substitute 3.91 for b in the equation. y=mx+ 3.91 In the table we have two ordered pairs. By substituting these into the Slope Formula we can find the slope.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,3.91) & ( 20,3.81)

m=3.81- 3.91/20- 0

▼

Simplify right-hand side

Subtract terms

m=- 0.1/20

Use a calculator

m=- 0.005

Therefore, the linear model can be written as follows. y= - 0.005x+3.91

b We will use our linear model to estimate the men's world record in the year 2000 and to predict the record for the year 2020.

Year 2000

Since 2000 is 40 years after 1960, it corresponds to x= 40. As a consequence, we will substitute 40 for x in the linear model to find the estimation.

y=- 0.005x+3.91

x= 40

y=- 0.005( 40)+3.91

(- a)b = - ab

y=- 0.2+3.91

Add terms

y=3.71

Therefore, the estimated men's world record of the year 2000 is 3.71 minutes.

Year 2020

The year 2020 is 60 years after 1960. To find the predicted world record for this year we will substitute 60 for x in the linear model.

y=- 0.005x+3.91

x= 60

y=- 0.005( 60)+3.91

(- a)b = - ab

y=- 0.3+3.91

Add terms

y=3.61

Therefore, the model predicts that the men's world record for the year 2020 is 3.61 minutes.

Subchapter links

Communicate Your Answer p.175

Monitoring Progress p.177-178

Exercises p.179-180