Question 1184143
<pre>
y = \large -\frac{3}{2} x + 1. 

That coding doesn't work on here.  But you meant this:

{{{y}}}{{{""=""}}}{{{expr(3/2)x+1}}}

Comparing that to y = mx+b we see that the slope, m = 3/2.

A line perpendicular to it has the slope which is the
reciprocal of that slope with the sign changed.

So the slope of the desired line is  m = -2/3

We use the point-slope form, which is:

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

{{{y-(-4)}}}{{{""=""}}}{{{expr(-2/3)(x-0)}}}

When we simplify the point-slope form, we will have the
slope-intercept form: 

{{{y+4}}}{{{""=""}}}{{{expr(2/3)(x)}}}

{{{y}}}{{{""=""}}}{{{expr(2/3)x-4}}}

Edwin</pre>