Question

Consider the line y=x+3.Find the equation of the line that is parallel to this line and passes through thepoint (-6, -3).Find the equation of the line that is perpendicular to this line and passes throughthe point (-6, -3).

Answer 1

Given:

Consider the line y=x+3.

Required:

We want to Find the equation of the line that is parallel to this line and passes through the point (-6, -3).

Find the equation of the line that is perpendicular to this line and passes through the point (-6, -3)

Explanation:

To find parallel to this line and passes through the point (-6, -3)

The slope is same for parallel line is 1

$\begin{gathered} y-(-3)=1(x-(-6)) \\ y+3=x+6 \\ y=x+3 \end{gathered}$

Which is same so there is no parallel line of given line which is passes through point (-6, -3)

Now to find the perpendicular to the given line

for this the slope of this line is -1

$\begin{gathered} y+3=-x-6 \\ y=-x-9 \end{gathered}$

Final answer:

y=x+3

y=-x-9