Answer:
x + y = -2
Explanation:
The given equation is y = -x - 5 and is of the form y = mx + c
Comparing y = -x - 5 with y = mx + c
the slope, m = -1
Two parallel lines always have equal slope
The line parallel to y = -x - 5 will also have a slope, m = -1
The line passes through the point (-1, -1)
The point-slope form of the equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute x₁ = -1, y₁ = -1, m = -1 into the point-slope equation above
[tex]\begin{gathered} y-(-1)\text{ = -1(x-(-1))} \\ y+1\text{ = -1(x+1)} \\ y\text{ + 1 = -x - 1} \\ y\text{ = -x - 1 - 1} \\ y\text{ = -x - 2} \\ x\text{ +y = -2} \end{gathered}[/tex]
The equation passing through (-1, -1) and passing through y=-x-5 is:
x + y = -2
