Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
10th Edition
ISBN: 9780134673301
Author: Waits, Foley, Kennedy, Bock Demana
Publisher: PEARSON
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Chapter P.4, Problem 45E
Solution

a.

The value of m and b .

  m=3187.5, b=42 000

Given:

The person purchased a house 8 years ago for $42 000 and this year it was appraised at $67 500 .

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:

Let initially at t=0 , the value of the house was V=$42 000 , so the corresponding point is t,V=0,  42 000 .

Since now after 8 years the value of house is $67 500 , the corresponding ordered pair is t,V=8,  67 500 .

In order to find the slope-intercept form the of line passing through the points 0,  42 000 and 8,  67 500 , first find the slope of the line using the slope formula as shown below:

  m=y2−y1x2−x1=67500−420008−0=25 5008=3187.5

Now substitute m=3187.5 and x,y=0, 42 000 in the general equation of line and solve for b as shown below:

  y=mx+b42000=3187.50+b42000=0+b⇒b=42000

Thus, in slope of the given linear equation is m=3187.5 and the y -intercept is b=42 000 .

b.

The years after purchase this house will be worth $72 500 .

  After 9.57 years

Given:

The person purchased a house 8 years ago for $42 000 and this year it was appraised at $67 500 .

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 plot the graph of the function, plot the points 0,  42 000 and 8,  67 500 , and connect them with a straight line.

Then to trace the years after purchase when the house will be worth $72 500 , draw a horizontal line at y=72 500 as shown in below graph,

  Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition, Chapter P.4, Problem 45E

Thus, the house will be worth $72 500 about 9.57 years after purchase.

c.

The number of years after purchase this house will be worth $74 000

  3187.5 t+42000=74000t=10.04

Given:

The person purchased a house 8 years ago for $42 000 and this year it was appraised at $67 500 .

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:

Since the slope of the given linear equation is m=3187.5 and the y -intercept is b=42 000 , the linear equation is

  V=3187.5 t+42000

Now in order to find the year when the house will be worth $74 000 , substitute V=74 000 into above equation and simplify further as shown below

  V=3187.5 t+4200074000=3187.5 t+420003187.5 t=74000−420003187.5 t=32000 t=320003187.5t≈10.04

Thus, the house will be worth $74 000 about 10.04 years after purchase.

d.

The number of years after purchase this house will be worth $80 250

  12 years

Given:

The person purchased a house 8 years ago for $42 000 and this year it was appraised at $67 500 .

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:

Since the slope of the given linear equation is m=3187.5 and the y -intercept is b=42 000 , the linear equation is

  V=3187.5 t+42000

Now in order to find the year when the house will be worth $80 250 , substitute V=80 250 into above equation and simplify further as shown below

  V=3187.5 t+4200080 250=3187.5 t+420003187.5 t=80 250−420003187.5 t=38 250 t=38 2503187.5t=12

Thus, the house will be worth $80 250 about 12 years after purchase.

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Chapter P.4, Problem 44E
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Chapter P.4, Problem 46E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

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What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY