Question 999556
(4,-3); 2x-7y=14


Solve for y and adjust into slope intercept form.
{{{-7y=-2x+14}}}
{{{y=(2/7)x-2}}}
Slope is {{{2/7}}}.


Determine what is negative reciprocal of {{{2/7}}}.
That would be  {{{-7/2}}}, and this is the slope of the line PERPENDICULAR to the given {{{2x-7y=14}}}.


Line to be found, if in slope-intercept form is  {{{y=-(7/2)x+b}}} and you want to find b.
{{{y+(7/2)x=b}}}
{{{b=y+(7/2)x}}}
Use the point which this line must pass through.
{{{b=(-3)+(7/2)4}}}
{{{b=-3+14}}}
{{{b=11}}}
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Line sought, in slope-intercept form is {{{highlight(y=-(7/2)x+11)}}}.  THIS LINE is perpendicular to 2x-7y=14 and passes through the required point (4,-3).


Adjust the line into standard form, IF YOU WANT, since your given line was in standard form.
{{{y=-(7/2)x+11}}}
{{{2y=-7x+22}}}
{{{2y+7x=22}}}
{{{highlight(7x+2y=22)}}}


The two red-outlined equations are equivalent.