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Answer:
The equation of new line is: [tex]\mathbf{y=-\frac{1}{2}x-7}[/tex]
Step-by-step explanation:
We need to write an equation of the line that passes through the point (-2, -6) and is parallel to the line x + 2y = 8
We need to find slope m and y-intercept b for the new line.
First we need to find slope m of the new line.
The given line x+2y=8 is parallel to new line.
When lines are parallel, there slope is same.
First writing equation in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept
[tex]x+2y=8\\2y=-x+8\\y=-\frac{1}{2}x+\frac{8}{2}\\ y=-\frac{1}{2}x+4[/tex]
Now comparing with [tex]y=mx+b[/tex] the slope is : [tex]m=-\frac{1}{2}[/tex]
Now finding y-intercept b
Using point (-2,-6) and slope [tex]m=-\frac{1}{2}[/tex] we can find y-intercept
[tex]y=mx+b\\-6=-\frac{1}{2}(-2)+b\\-6=1+b\\b=-6-1\\b=-7[/tex]
So, we get y-intercept b = -7
Now the equation of required line having slope [tex]m=-\frac{1}{2}[/tex] and y-intercept b = -7 is:
[tex]y=mx+b\\y=-\frac{1}{2}x-7[/tex]
So, the equation of new line is: [tex]\mathbf{y=-\frac{1}{2}x-7}[/tex]