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

10th Edition

ISBN: 9780134673301

Author: Waits, Foley, Kennedy, Bock Demana

Publisher: PEARSON

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Expert Solution & Answer

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 4x−3y=5 .

Formula used:

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.

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 4x−3y=5 , use the fact that two parallel equations has equal slopes.

Since the slope of the line is equal to the line 4x−3y=5 , so find the slope of this equation by writing it in the form, y=mx+c , here m is slope, as

4x−3y=53y=4x−5y=134x−5y=43x−53

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=43−6+cc−4×2=3c−8=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=−34x−32

Given information:

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

Formula used:

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.

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 4x−3y=5 , use the fact that the multiplication of slope of two perpendicular lines is equals to −1 .

First, find the slope of the line 4x−3y=5 by writing it’s equation in the form, y=mx+c , here m is slope, as

4x−3y=53y=4x−5y=134x−5y=43x−53

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=−34−6+cc+34×6=3c+92=3c=3−92c=6−92c=−32

Thus, the slope intercept form of the line is

y=−34x−32

Chapter P, Problem 33RE

Chapter P, Problem 35RE

Chapter P Solutions

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

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Solution Summary: The author explains the equation of the line in slope-intercept form that passes through the point (-6,3) and is parallel to 4x-3y=5.

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Chapter P Solutions