Respuesta :
Answer:
Part A:
[tex]y=-x+8[/tex]Part B:
[tex]y=x+4[/tex]Step-by-step 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:
[tex]m_a=-1[/tex]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:
[tex]\begin{gathered} y-6=-1(x-2) \\ \rightarrow y-6=-x+2 \\ \\ \Rightarrow y=-x+8 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=-x+8[/tex]Part B:
Remember that the product between the slopes of two perpendicular lines is -1. This way, we'll have that:
[tex]\begin{gathered} -1\times m_2=-1 \\ \\ \Rightarrow m_2=1 \end{gathered}[/tex]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:
[tex]\begin{gathered} y-6=(x-2) \\ \rightarrow y=x+4 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=x+4[/tex]