PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Estimation
A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.
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Chapter P.4, Problem 68E
Solution

a.

The graph of y=mx for m=−3, −2, −1, 1, 2, 3 in the window −8,8 by −5,5 .

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 68E , additional homework tip 1

Given:

The equation, y=mx for m=−3, −2, −1, 1, 2, 3

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 graph of the equation for different values of m is shown below:

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 68E , additional homework tip 2

All the graph pass through the origin, so the x -intercept and y -intercept of the graphs is same.

Since m represents the slop of the linear equation, the slopes of all the lines are different.

b.

If m>0 , what do the graph of y=mx and y=−mx have in common.

The graphs have the same x -intercepts but one is increasing from left to right and other is decreasing.

Given:

The equation, y=mx and y=−mx for m>0 .

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 graphs have the same x -intercepts but one is increasing from left to right and other is decreasing.

c.

The graph for y=0.3x+b for b=−3,−2, −1, 0, 1, 2, 3 in the window −8,8 by −5,5 ..

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 68E , additional homework tip 3

Given:

The equation, y=0.3x+b for b=−3, −2, −1, 0,  1, 2, 3

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 graphs for the different values of b are shown below:

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 68E , additional homework tip 4

The graphs have the same slope but different y -intercepts.

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Chapter P.4, Problem 67E
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Chapter P.4, Problem 69E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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