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Equation for Perpendicular Line










































Find the equation of the straight line that is perpendicular to the line 3x + 5y = 7 and passes through the point (-1, 4).

Use this information to answer the questions.

The slope of the new line is:

Comments for Equation for Perpendicular Line

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Sep 29, 2013
Perpendicular Line
by: Staff


Answer

Part I


Find the equation of the straight line that is perpendicular to the line 3x + 5y = 7 and passes through the point (-1, 4).


3x + 5y = 7 is the standard form of the equation

rewrite equation in slope-intercept form:

y = mx + b


3x + 5y = 7 is the standard form of the equation

rewrite equation in slope-intercept form: 

      y = mx + b





3x + 5y = 7

subtract 3x from each side of the equation

3x + 5y - 3x = 7 - 3x

3x - 3x + 5y = 7 - 3x

0 + 5y = 7 - 3x

5y = 7 - 3x


subtract 3x from each side of the equation





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Sep 29, 2013
Perpendicular Line
by: Staff


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Part II


divide each side of the equation by 5

5y = - 3x + 7

5y / 5 = (- 3x + 7) / 5

y = (- 3x + 7) / 5

y = (- 3/5)x + 7/5


divide each side of the equation by 5





the slope intercept form of the equation is

y = (- 3/5)x + 7/5



the slope-intercept form of the equation








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Sep 29, 2013
Perpendicular Line
by: Staff


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Part III


The slope of a line perpendicular to this equation is:

m = (-1) * (the reciprocal of -3/5)

m = (-1) * (-3/5)⁻¹


m = (-1) * (-5/3)

m = 5/3


the slope of a line which is perpendicular to the original equation





the slope intercept form of the perpendicular line is:

y = mx + b

y = (5/3)x + b



 the slope-intercept form of the equation for the perpendicular line






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Sep 29, 2013
Perpendicular Line
by: Staff


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Part IV


Since the perpendicular line passes through the point (-1, 4), you can use this point to solve for b.

(-1, 4) means that when x = -1, then y = 4



use the point (-1, 4) to solve for the value of b




Substitute the values for x and y into the equation for the perpendicular line, and then solve for b.

y = (5/3)x + b

4 = (5/3) * (-1) + b

4 = (-5/3) + b


substitute known values for x and y







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Sep 29, 2013
Perpendicular Line
by: Staff


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Part V


add 5/3 to each side of the equation

4 + 5/3 = (-5/3) + b + 5/3

4 + 5/3 = (-5/3) + 5/3 + b

4 + 5/3 = 0 + b

4 + 5/3 = b

b = 4 + 5/3


b = (4)*(3/3) + 5/3

b = 12/3 + 5/3

b = 17/3, or 5 2/3



 add 5/3 to each side of the equation





substitute the value of b into the equation for the perpendicular line

y = (5/3)x + b

b = 17/3

y = (5/3)x + 17/3



substitute the value of b into the equation for the perpendicular line






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Sep 29, 2013
Perpendicular Line
by: Staff


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Part VI


The final equation for the perpendicular line which passes through the point (-1, 4) is:

y = (5/3)x + 17/3

m = slope = 5/3

b = slope intercept = 17/3



final equation for the perpendicular line which passes through the point  (-1, 4)





The standard form of the perpendicular line can be determined as follows:

3 * y = 3 * ((5/3)x + 17/3)

3y = 5x + 17

3y - 5 x = 5x + 17 - 5x

- 5 x + 3y = 5x - 5x + 17

- 5 x + 3y = 0 + 17

- 5 x + 3y = 17

standard form of the perpendicular line

- 5x + 3y = 17


a graph of both equations is shown below:






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Sep 29, 2013
Perpendicular Line
by: Staff


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Part VII


 a graph of both equations is shown: 

1.  original equation

      3x + 5y = 7 

2.  equation for the perpendicular line which passes through the point  (-1, 4) 

      - 5x + 3y = 17







Thanks for writing.

Staff
www.solving-math-problems.com


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