Question 616044
Given
Point (x, y)=(-1,3) 
Line:
x+2y=-6
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Arrange the given line according to the slop-intercept form
x+2y=-6
2y=-x-6
Divide by 2 both sides
2y/2=(-x-6)/2
y=((-x)/2)-(6/2)

y=(-x/2)x+6/2
y=(-1/2)x-3
Compare above equation with the equation of line slope-intercept form
y=mx+b

m=-1/2 and b=-3
Slope of the given line m = -1/2 and y-intercept = b = -3
Since given line is parallel to the required line; slopes of the both line will be same.
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Now we have a point (-1,3) and slope (-1/2) of the required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line
y=mx+b
3=(-1/2)(-1)+b
3=1/2+b
3-1/2=b
Take LCD
(6-1)/2=b
5/2=b
y-intercept of the required line =b=5/2
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Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form
y=mx+b
y=(1/2)x+(5/2)
y=x/2+5/2
Above equation is the required equation of the line in slope-intercept form.

Graph
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Given Line Green
Required Line Red
{{{ graph(500,500,-10,10,-10,10,x/2+5/2,x/2-3) }}}