Question

Question 10 of 183Consider the line y = -x +6.(a) Find the equation of the line that is parallel to this line and passes through the point (2, 6).(b) Find the equation of the line that is perpendicular to this line and passes through the point (2, 6).Note that a graphing calculator may be helpful in checking your answer.

Answer 1

Part A:

`y=-x+8`

Part B:

`y=x+4`

Explanation:

Part A:

Remember that two parallel lines have the same slope. This way, we can conclude that the slope of this particular line is:

`m_a=-1`

Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:

`\begin{gathered} y-6=-1(x-2) \\ \rightarrow y-6=-x+2 \\ \\ \Rightarrow y=-x+8 \end{gathered}`

Therefore, we can conclude that the equation of this line is:

`y=-x+8`

Part B:

Remember that the product between the slopes of two perpendicular lines is -1. This way, we'll have that:

`\begin{gathered} -1* m_2=-1 \\ \\ \Rightarrow m_2=1 \end{gathered}`

Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:

`\begin{gathered} y-6=(x-2) \\ \rightarrow y=x+4 \end{gathered}`

Therefore, we can conclude that the equation of this line is:

`y=x+4`