Question 119072
The given line 
{{{2x+4y=-7}}} 
can be modified to the slope-intercept form.
{{{4y=-2x-7}}} 
{{{y=-2x/4-7/4}}} 
{{{y=-x/2-7/4}}} 
The given line has a slope, 
{{{m=-1/2}}}
Perpendicular lines have slopes that are negative reciprocals of each other.
{{{m[1]m[2]=-1}}}
The slope of the new line is then
{{{(-1/2)m[2]=-1}}}
{{{m[2]=2}}}
You can then use the point-slope form of a line.
{{{y-y[1]=m(x-x[1])}}}
{{{y-(-2)=2(x-(-3))}}}
{{{y+2=2(x+3)}}}
{{{y+2=2x+6}}}
{{{highlight(y=2x+4)}}}
Check your answer using your point.
{{{y=2x+4}}}
{{{-2=2(-3)+4}}}
{{{-2=-6+4}}}
{{{-2=-2}}}
True statement.
Good answer.