Question 161179
Write an equation of the line that passes through the point at (4,4) and is perpendicular to the line whose equation is 2x+y=7.



since given line {{{2x+y=7}}} which contains point ({{{4}}},{{{4}}}), we will find a line perpendicular to {{{2x+y=7}}} using what we know: 
{{{2x+y=7}}} we can write in the slope-intercept form as {{{y= - 2x +7}}}
the slopes of the perpendicular lines are negative reciprocal; so  the slope {{{m[p]}}} is negative reciprocal of the slope {{{m}}} from the line{{{ y= - 2x +7)}}}, or {{{-(1/m)}}}

since {{{m=-2}}}  , the slope of the unknown line must be;
 
 {{{m[p] = -(1/m)}}}

{{{m[p] = -(1)/(-2)= 1/2)}}}

we also know that line goes through ({{{4}}},{{{4}}}), and we can find the equation by plugging in this info into the {{{point-slope}}} formula

Point-Slope Formula:

{{{y-y1=m(x-x1)}}} where m is the slope and ({{{x1}}},{{{y1}}}) is the given point({{{4}}},{{{4}}})

Plug in, {{{x1=4}}} and {{{y1=4}}}, 

{{{y-4=(1/2 )(x-4)}}}

{{{y-4= (1/2 )x -(1/2 )( 4)}}}

{{{y-4= (1/2 )x -2}}}

{{{y= (1/2 )x -2 + 4}}}

{{{y= (1/2 )x + 2}}}

Here is the graph:
{{{2x+y=7}}} and {{{- (1/2 )x + y = 2}}}

From the graph you can see that red line {{{- (1/2 )x + y = 2}}} contains  point ({{{4}}},{{{4}}})

*[invoke solve_by_graphing "-(1/2 )", 1, 2, 2, 1, 7]