Answer:
1. [tex]y=\dfrac{1}{5}x-\dfrac{32}{5}[/tex]
2. [tex]y=-5x+30[/tex]
Step-by-step explanation:
The line [tex]y=-5x+5[/tex] has the slope [tex]m_1=-5[/tex]
1. Perpendicular line to the given line has the slope [tex]m_2[/tex] for which
[tex]m_1\cdot m_2=-1,[/tex]
so
[tex]-5\cdot m_2=-1\\ \\m_2=\dfrac{1}{5}[/tex]
Hence, the equation of the perpendicular line passing through the point (7,-5) is
[tex]y-(-5)=\dfrac{1}{5}(x-7)\\ \\y+5=\dfrac{1}{5}x-\dfrac{7}{5}\\ \\y=\dfrac{1}{5}x-\dfrac{32}{5}[/tex]
2. Parallel line to the given line has the slope [tex]m_3[/tex] for which
[tex]m_3=m_1,[/tex]
so
[tex]m_3=-5[/tex]
Hence, the equation of the parallel line passing through the point (7,-5) is
[tex]y-(-5)=-5(x-7)\\ \\y+5=-5x+35\\ \\y=-5x+30[/tex]
