Answer:
- [tex]y = -\frac{4}{5} x - \frac{14}{5}[/tex]
- [tex]y = \frac{5}{4} x -11[/tex]
Step-by-step explanation:
Given line ;
[tex]y = \frac{5}{4} x -3\\\\m = slope\\m = \frac{5}{4}[/tex]
1. Perpendicular and passes through (4,-6)
[tex]m_1 = \frac{5}{4} \\\\m_2 = \frac{-1}{m_1} \\\\m_2 = \frac{-1}{\frac{5}{4} } \\\\m_2 = -\frac{4}{5} \\\\(4,-6)=(x ,y)\\[/tex]
Substitute the values above into slope intercept form ; y=mx+b and solve for b.
[tex]y =mx+b\\\\-6 = -\frac{4}{5} (4) + b\\\\-6 = -\frac{16}{5} + b\\\\-6 + \frac{16}{5} = b\\\\-\frac{14}{5} = b\\\\b = -\frac{14}{5}\\\\m = - \frac{4}{5}[/tex]
Substitute new values into ; y =mx+b.
[tex]y = -\frac{4}{5} (x)- (\frac{14}{5} )\\\\y = -\frac{4}{5} x - \frac{14}{5}[/tex]
2.Parallel and passes through (4,-6)
[tex]m = \frac{5}{4} \\\\(4,-6)=(x_1,y_1)[/tex]
Substitute values into point slope form and simplify
[tex]y-y_1=m(x-x_1)\\\\y - (-6) = \frac{5}{4} (x -4)\\\\y+6 = \frac{5}{4} x -5\\\\y = \frac{5}{4} x -5-6\\\\y = \frac{5}{4} x -11[/tex]
