PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P, Problem 34RE
Solution

a.

The equation of the line in slope-intercept form with given equation.

  y=43x+11

Given information:

The line passes through the point 6,3 and is parallel to the line 4x3y=5 .

Formula used:

  1. The equation of the lie in slope-intercept form that passes through a point x1,y1 with a slope m is given as: y=mx+c, where c can be find putting the point in the equation.
  2. The slope of two parallel lines are equal.

Calculation:

To find the slope intercept form use the point-slope form of equation of line that passes through point 6,3 , and is parallel to the line 4x3y=5 , use the fact that two parallel equations has equal slopes.

Since the slope of the line is equal to the line 4x3y=5 , so find the slope of this equation by writing it in the form, y=mx+c , here m is slope, as

  4x3y=53y=4x5y=134x5y=43x53

Comparing above equation with y=mx+c gives the slope of this equation,

  m=43

Thus, the equation of the line can be written by using

  y=mx+cy=43x+c

Now, since the line passes through the point 6,3 putting it in place of x,y find c as

  3=436+cc4×2=3c8=3c=3+8c=11

Thus, the slope intercept form of the line is

  y=43x+11

b.

The equation of the line in slope-intercept form with given equation.

  y=34x32

Given information:

The line passes through the point 6,3 and is perpendicular to the line 4x3y=5 .

Formula used:

  1. The equation of the lie in slope-intercept form that passes through a point x1,y1 with a slope m is given as: y=mx+c, where c can be find putting the point in the equation.
  2. The multiplication of slope of two perpendicular lines is equals to 1 .

Calculation:

To find the slope intercept form use the point-slope form of equation of line that passes through point 6,3 , and is perpendicular to the line 4x3y=5 , use the fact that the multiplication of slope of two perpendicular lines is equals to 1 .

First, find the slope of the line 4x3y=5 by writing it’s equation in the form, y=mx+c , here m is slope, as

  4x3y=53y=4x5y=134x5y=43x53

Comparing above equation with y=mx+c gives the slope of this equation,

  m=43

Now find the slope of the line perpendicular to this line, since the the multiplication of slope of two perpendicular lines is equals to 1 , so the slope of the line, say m2 can be find as

  m×m2=143×m2=1m2=143m2=34

Thus, the equation of the line can be written by using

  y=m2x+cy=34x+c

Now, since the line passes through the point 6,3 putting it in place of x,y find c as

  3=346+cc+34×6=3c+92=3c=392c=692c=32

Thus, the slope intercept form of the line is

  y=34x32

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. P.1 - Prob. 1ECh. P.1 - Prob. 2ECh. P.1 - Prob. 3ECh. P.1 - Prob. 4ECh. P.1 - Prob. 5ECh. P.1 - Prob. 6ECh. P.1 - Prob. 7ECh. P.1 - Prob. 8ECh. P.1 - Prob. 9ECh. P.1 - Prob. 10ECh. P.1 - Prob. 11ECh. P.1 - Prob. 12ECh. P.1 - Prob. 13ECh. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - Prob. 17ECh. P.1 - Prob. 18ECh. P.1 - Prob. 19ECh. P.1 - Prob. 20ECh. P.1 - Prob. 21ECh. P.1 - Prob. 22ECh. P.1 - Prob. 23ECh. P.1 - Prob. 24ECh. P.1 - Prob. 25ECh. P.1 - Prob. 26ECh. P.1 - Prob. 27ECh. P.1 - Prob. 28ECh. P.1 - Prob. 29ECh. P.1 - Prob. 30ECh. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Prob. 33ECh. P.1 - Prob. 34ECh. P.1 - Prob. 35ECh. P.1 - Prob. 36ECh. P.1 - Prob. 37ECh. P.1 - Prob. 38ECh. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Prob. 42ECh. P.1 - Prob. 43ECh. P.1 - Prob. 44ECh. P.1 - Prob. 45ECh. P.1 - Prob. 46ECh. P.1 - Prob. 47ECh. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. P.1 - Prob. 50ECh. P.1 - Prob. 51ECh. P.1 - Prob. 52ECh. P.1 - Prob. 53ECh. P.1 - Prob. 54ECh. P.1 - Prob. 55ECh. P.1 - Prob. 56ECh. P.1 - Prob. 57ECh. P.1 - Prob. 58ECh. P.1 - Prob. 59ECh. P.1 - Prob. 60ECh. P.1 - Prob. 61ECh. P.1 - Prob. 62ECh. P.1 - Prob. 63ECh. P.1 - In Exercises 63 and 64, use scientific notation to...Ch. P.1 - Prob. 65ECh. P.1 - Prob. 66ECh. P.1 - Prob. 67ECh. P.1 - Prob. 68ECh. P.1 - Prob. 69ECh. P.1 - Prob. 70ECh. P.1 - Prob. 71ECh. P.1 - Prob. 72ECh. P.1 - Prob. 73ECh. P.1 - Prob. 74ECh. P.1 - Prob. 75ECh. P.1 - Prob. 76ECh. P.2 - Prob. 1QRCh. P.2 - Prob. 2QRCh. P.2 - Prob. 3QRCh. P.2 - Prob. 4QRCh. P.2 - Prob. 5QRCh. P.2 - Prob. 6QRCh. P.2 - Prob. 7QRCh. P.2 - Prob. 8QRCh. P.2 - Prob. 9QRCh. P.2 - Prob. 10QRCh. P.2 - Prob. 1ECh. P.2 - Prob. 2ECh. P.2 - Prob. 3ECh. P.2 - Prob. 4ECh. P.2 - Prob. 5ECh. P.2 - Prob. 6ECh. P.2 - Prob. 7ECh. P.2 - Prob. 8ECh. P.2 - Prob. 9ECh. P.2 - Prob. 10ECh. 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