Your question sounds incomplete. As you missed to add the diagram. The diagram is attached below.
Answer:
The equation of the line that is parallel to the given line and passes through the point (−4,−6 ) will be:
[tex]y=-6[/tex]
Step-by-step explanation:
From the diagram, the given points are
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-8,\:4\right),\:\left(x_2,\:y_2\right)=\left(8,\:4\right)[/tex]
[tex]m=\frac{4-4}{8-\left(-8\right)}[/tex]
[tex]m=0[/tex]
so the equation of line becomes
[tex]y-y_1=m\left(x-x_1\right)[/tex]
As the equation of a line passes through (−4,−6 ).
so
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]0\cdot \left(x+4\right)=y-\left(-6\right)[/tex]
[tex]\mathrm{Apply\:rule}\:0\cdot \:a=0[/tex]
[tex]0=y-\left(-6\right)[/tex]
[tex]0=y+6[/tex]
[tex]y=-6[/tex]
Therefore, the equation of the line that is parallel to the given line and passes through the point (−4,−6 ) will be:
[tex]y=-6[/tex]
