Question 1189603
What is an equation in slope-intercept form of the line that 
passes through (6, −7) and is perpendicular to the line shown 
below?
<pre>
I'll make up a line shown below, since you didn't give one.
Your problem will be done the same way:

Let's say you were given this graph:

{{{drawing(400,6800/21,-5,15,-12,5,line(-10,0,20,0),line(0,-15,0,10),
locate(-4.3,1.8,"(-2,2)"),circle(-2,2,.2),circle(-2,2,.2),
circle(-2,2,.1),
circle(-2,2,.15),
circle(-2,2,.12),
locate(6,-7,"(6,-7)"),locate(6,-7,"(6,-7)"),

locate(10,-3.1,"(10,-4)"),circle(10,-4,.2),circle(10,-4,.2),circle(10,-4,.1),circle(10,-4,.15),circle(10,-4,.12),
line(-12,6.95,16,-7.05), circle(6,-7,.2),circle(6,-7,.1),circle(6,-7,.15),circle(6,-7,.05)


)}}}

We take two points on the given line and find its slope:

Slope formula:

{{{m}}}{{{""=""}}}{{{(y[2]-y[1])/(x[2]-x[1])}}}

where (x<sub>1</sub>,y<sub>1</sub>) = (-2,2)
and where (x<sub>2</sub>,y<sub>2</sub>) = (10,-4)

{{{m}}}{{{""=""}}}{{{((-4)-(2))/((10)-(-2))}}}

{{{m}}}{{{""=""}}}{{{(-4-2)/(10+2)}}}

{{{m}}}{{{""=""}}}{{{(-6)/(12)}}}

{{{m}}}{{{""=""}}}{{{-1/2}}}

That's the slope of the given line. A line perpendicular
to a given line has a slope which is the reciprocal of
the given line with the opposite sign.

The reciprocal of {{{-1/2}}} with the opposite sign is {{{""+2/1}}},
which is just 2.

Next we use the point-slope formula:
y - y<sub>1</sub> = m(x - x<sub>1</sub>)
where (x<sub>1</sub>,y<sub>1</sub>) = (6,-7), and m = 2.

{{{y-(-7)}}}{{{""=""}}}{{{(2)(x-(6))}}}
{{{y+7}}}{{{""=""}}}{{{2(x-6)}}}
{{{y+7}}}{{{""=""}}}{{{2x-12}}}
{{{y}}}{{{""=""}}}{{{2x-19}}}   <---answer

Now use the above as a model to solve yours. 
Here's the graph of the answer (in green): 

{{{drawing(400,6800/21,-5,15,-12,5,line(-10,0,20,0),line(0,-15,0,10),
locate(-4.3,1.8,"(-2,2)"),circle(-2,2,.2),circle(-2,2,.2),
circle(-2,2,.1),
circle(-2,2,.15),
circle(-2,2,.12),

green(line(-6,-31,16,13)),
locate(10,-3.1,"(10,-4)"),circle(10,-4,.2),circle(10,-4,.2),circle(10,-4,.1),circle(10,-4,.15),circle(10,-4,.12),
line(-12,6.95,16,-7.05), locate(6,-7,"(6,-7)"),circle(6,-7,.2),circle(6,-7,.1),circle(6,-7,.15),circle(6,-7,.05)


)}}}


Edwin</pre>