Answer:
The required equation is: [tex]\mathbf{x+2y=-16}[/tex]
Step-by-step explanation:
We need to find equation of the line that passes through the point (-4, -6) and is  perpendicular to the line
The equation of line will be in the slope intercept form [tex]y=mx+b[/tex]
where m is slope and b is y-intercept.
Finding Slope
First transforming the given equation [tex]2x -y = 6[/tex] in slope-intercept form:
[tex]2x -y = 6\\-y=-2x+6\\y=2x-6[/tex]
Now comparing the equation with general equation of slope intercept form We get slope m= 2
Since the two lines are perpendicular, the slope of new line will be opposite reciprocal of given line i.e [tex]m=-\frac{1}{m}[/tex]
So, Slope of required line is: [tex]m=-\frac{1}{2}[/tex]
Finding y-intercept
y-intercept can be found using slope [tex]m=-\frac{1}{2}[/tex] and point (-4,-6) as follows
[tex]y=mx+b\\-6=-\frac{1}{2}(-4)+b\\-6=+2+b\\b=-6-2\\b=-8[/tex]
So, y-intercept b = -8
Finding equation of line:
The equation of line having slope [tex]m=-\frac{1}{2}[/tex] and y-intercept b = -8 is:
[tex]y=mx+b\\y=-\frac{1}{2}(x)-8[/tex]
Now, writing the equation in standard form i.e Ax+By=C
[tex]y=-\frac{1}{2}(x)-8 \\ Multiply \ by \ 2\\2y=-x-16\\x+2y=-16[/tex]
So, the required equation is: [tex]\mathbf{x+2y=-16}[/tex]
