Question 432922
We know that two lines are perpendicular when the product of their slopes is -1.

First we write 4x+2y=3 in the slope-intercept form:{{{y=-2x+3/2}}}, we see that 

the slope of this line is m1=-2. Let's the slope of the perpendicular line, m2, 

then m1*m2=-1, substitute m1=-2, (-2)*m2=-1 => m2=1/2.

Now we find the equation of line through the point (-1, 6) with slope m2=1/2:

{{{y-6=(1/2)*(x+1)}}}, write it in the slope-intercept form.

{{{y=(1/2)*x+7}}}, and in the standard form:

{{{x-2y=-14}}}

{{{graph(300, 300, -15, 5, -5, 10, -2x+(3/2), (1/2)x+7)}}}

Done.