Question

What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )?

x = −6
x = −4
y = −6
y = −4

Answer 1

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:

`y=-6`

Explanation:

From the diagram, the given points are

• ( -8 , 4 )

• ( 8 , 4 )

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-8,\:4\right),\:\left(x_2,\:y_2\right)=\left(8,\:4\right)`

`m=(4-4)/(8-\left(-8\right))`

`m=0`

so the equation of line becomes

`y-y_1=m\left(x-x_1\right)`

As the equation of a line passes through (−4,−6 ).

so

`y-y_1=m\left(x-x_1\right)`

`\mathrm{Apply\:rule}\:-\left(-a\right)=a`

`0\cdot \left(x+4\right)=y-\left(-6\right)`

`\mathrm{Apply\:rule}\:0\cdot \:a=0`

`0=y-\left(-6\right)`

`0=y+6`

`y=-6`

Therefore, the equation of the line that is parallel to the given line and passes through the point (−4,−6 ) will be:

`y=-6`