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neonofarm [45]
3 years ago
5

Please help me,I give up on this.i just don’t get it.

Mathematics
1 answer:
Stolb23 [73]3 years ago
8 0

Answer:

  1. y = -\frac{4}{5} x - \frac{14}{5}
  2. y = \frac{5}{4} x -11

Step-by-step explanation:

Given line ;

y = \frac{5}{4} x -3\\\\m = slope\\m = \frac{5}{4}

1. Perpendicular and passes through (4,-6)

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)\\

Substitute the values above into slope intercept form ; y=mx+b and solve for b.

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}

Substitute new values into ; y =mx+b.

y = -\frac{4}{5} (x)- (\frac{14}{5} )\\\\y = -\frac{4}{5} x - \frac{14}{5}

2.Parallel and passes through (4,-6)

m = \frac{5}{4} \\\\(4,-6)=(x_1,y_1)

Substitute values into point slope  form and simplify

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

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