Question 1203422
.
Write an equation in slope-intercept form for the line that passes through the given point 
and is perpendicular to the graph of the given equation. (4, -5), 2x-5y= -10
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<pre>
The given line 

    2x - 5y = -10

is the same as

    y = {{{(2/5)x + 2}}}.


It has the slope  {{{2/5)}}}.
A perpendicular line has the slope  {{{(-5/2)}}}  (opposite reciprocal),
so an equation of any perpendicular line is 

    y = {{{(-5/2)x + c}}}.    (1)


Here "c" is some constant, now unknown, which we should determine.

To do it, we substitute coordinates (4,-5) of the given point into equation (1).  It gives us

    -5 = {{{(-5/2)*4+c}}},

or

    -5 = -10 + c,

    c = 10 - 5 = 5.


So, the final equation of the perpendicular line through (4,-5) is

    y = {{{(-5/2)x+5}}}

in slope-intercept form.
</pre>

Solved.


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In this site, &nbsp;there is a group of lessons related to this class of problems

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Find-the-slope-of--a-straight-line-passing-through-two-given-points.lesson>Find the slope of a straight line in a coordinate plane passing through two given points</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Equation-for--a-straight-line-having-a-given-slope-and-passing-through-a-given-point.lesson>Equation for a straight line having a given slope and passing through a given point</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Solving-problems-related-to-the-slope-of-a-straight-line.lesson>Solving problems related to the slope of a straight line</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Equation-for--a-straight-line-passing-through-two-given-points.lesson>Equation for a straight line in a coordinate plane passing through two given points</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Equation-for--a-straight-line-parallel-to-a-given-line-and-passing-through-a-given-point.lesson>Equation for a straight line parallel to a given line and passing through a given point</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Equation-for--a-straight-line-perpendicular-to-a-given-line-and-passing-through-a-given-point.lesson>Equation for a straight line perpendicular to a given line and passing through a given point</A> (*)


The most relevant to your current problem is the lesson marked &nbsp;(*) &nbsp;in the list.

So start from this lesson.


But if you want to learn the subject in all its aspects, &nbsp;then learn/read all these lessons.


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