PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P, Problem 33RE
Solution

a.

The scatter plot of the given data.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P, Problem 33RE , additional homework tip 1

Given:

The table shows for average SAT math score, y , in selected years x ,

    Year200820092010201120122013201420152016
    Annual Average cost514514515514514514513511508

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

The scatter plot of the given data is shown below:

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P, Problem 33RE , additional homework tip 2

b.

The linear equation for average SAT math score, y , in terms of the year x using the points 2008,514 and 2016,508 .

  y=−0.75x−2008+514

Given:

The table shows for average SAT math score, y , in selected years x ,

    Year200820092010201120122013201420152016
    Annual Average cost514514515514514514513511508

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the linear equation, first find the slope of the line using the points 2008,514 and 2016,508 as shown below

  m=y2−y1x2−x1=508−5142016−2008=−68=−0.75

Now, substitute m=−0.75 and x1,y1=2008,514 into the point-slope form of the line and simplify further as shown below

  y−y1=mx−x1y−514=−0.75x−2008y=−0.75x−2008+514

Thus, the linear equation for average SAT math score is y=−0.75x−2008+514 .

The graph on the scatter plot is shown below:

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P, Problem 33RE , additional homework tip 3

c.

The average SAT score in 2020 using the equation found in part (b).

  505

Given:

The linear equation that gives the average SAT score in year x is y=−0.75x−2008+514 .

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the average SAT score in 2020, substitute x=2020 into the given equation and simplify further as shown below

  y=−0.75x−2008+514=−0.752020−2008+514=−0.7512+514=−9+514=505

Thus, the average SAT score in 2020 is 505 .

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Chapter P, Problem 32RE
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Chapter P, Problem 34RE

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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