SOLUTION: Find the equation of the line passing through the point (6,3) that is perpendicular to the line 4x−5y=−10

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Question 1191010: Find the equation of the line passing through the point (6,3) that is perpendicular to the line 4x−5y=−10
Found 4 solutions by Alan3354, MathLover1, ikleyn, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
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Find the equation of the line passing through the point (6,3) that is perpendicular to the line 4x−5y=−10
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Step 1, find the slope of the given line, call it m1.
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The slope of lines perpendicular is the negative inverse of m1, which is -1/m1. Call that m.
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Step 2, use y-y1 = m*(x-x1) where (x1,y1) is the point (6,3)

Answer by MathLover1(20855) About Me  (Show Source):
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the equation of the line
y=mx%2Bb

find the line passing through the point (6,3)
that is perpendicular to the line 4x%E2%88%925y=%E2%88%9210
perpendicular lines have slopes negative reciprocal to each other
so, find a slope of 4x%E2%88%925y=%E2%88%9210
4x%2B10=5y

y=%284%2F5%29x%2B2-> slope is 4%2F5

perpendicular line will have a slope -1%2F%284%2F5%29=-5%2F4

y=-%285%2F4%29x%2Bb.....use given point to find b

3=-%285%2F4%296%2Bb
3%2B30%2F4=b
b=21%2F2

your equation is:
y=-%285%2F4%29x%2B21%2F2






Answer by ikleyn(53937) About Me  (Show Source):
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.

Read the lesson

    - Equation for a straight line perpendicular to a given line and passing through a given point

in this site and find there the complete explanation on how to do it.

From this lesson,  learn the subject once and for all.


At this site,  there is a group of lessons related to this class of problems
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point (*)

The most relevant to your current problem is the lesson marked  (*)  in the list.
So start from this lesson.

But if you want to learn the subject in all its aspects,  you need to learn all these lessons.

Consider them as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.



Answer by greenestamps(13367) About Me  (Show Source):
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The equation of any line perpendicular to the line 4x-5y=-10 will have the form 5x+4y=C for some constant C. Note that to get that form, the two coefficients are switched, and the sign is changed.

To get the equation you want, simply substitute the given values x=6 and y=3 to find the value of C.

5x+4y = 5(6)+4(3) = 30+12 = 42

ANSWER: 5x+4y=42