Question 1079202
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<pre>
For the given line, the x-intercept is x = {{{-1.5}}}  (it makes y = 0).


So, we need to find the equation of the line perpendicular to the given line and passing through the point (-1.5,0).


The given line has the slope 2 (because the equation of the given line in the slope-form is y = 2x+3).


Hence, the slope of the perpendicular line is -0.5.


The straight line with the slope -0.5 through the point (-1.5,0) is

y - 0 = (-0.5)*(x-(-1.5)),   or

y = -0.5*(x+1.5).


It is the same as 

2y = -(x+1.5),   or

4y = - 2x - 3,   or

2x + 4y + 3 = 0,


on your choice.
</pre>

<U>Solved</U>.   &nbsp;&nbsp;&nbsp;&nbsp;<U>And plotted</U>:


{{{graph( 330, 330, -5.5, 5.5, -5.5, 5.5,
          2x+3, -0.5*(x+1.5)
)}}}


Plot y = 2x+3  (red)  and  y = -0.5*(x+1.5) (green)