Question

Need help!
A. y= -x+2
B. y=2x+2
C. y=2x-1
D. y=5x+2

Answer 1

D) y=5x+2

Explanation:

Perpendicular means negative reciprocal of the slope.

So the slope must be 5.

y-y1=m(x-x1)

y-(-3)=5(x-(-1))

y+3=5(x+1)

y=5x+5-3

y=5x+2

Answer 2

`\large\boxed{y=5x+2}`

Explanation:

`\text{Let:}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ ||\ l\iff m_1=m_2\\\\k \perp l\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\==================================`

`\text{We have the equation of a line:}\\\\y=-(1)/(5)x+4\to m_1=-(1)/(5)\\\\\text{Therefore}\\\\m_2=-(1)/(-(1)/(5))=-\left(-(5)/(1)\right)=5\\\\\text{Initially, our equation has the form}\\\\y=5x+b`

`\text{The line should pass through point (-1, -3).}\\\text{We substitute the coordinates of the point into the equation:}\\\\-3=5(-1)+b\\-3=-5+b\qquad\text{add 5 to both sides}\\-3+5=-5+5+b\\2=b\to b=2\\\\\text{Finally:}\\\\y=5x+2`