Question

Write the equation of this line. A line that contains point (2, –2) and perpendicular to another line whose slope is –1.

Thanks!

Answer 1

`\text{Let}\\k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp k\iff m_1m_2=-1\\--------------------\\\text{We have}\\k:y=-1x+b_1\to m_1=-1\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff-1m_2=-1\quad|:(-1)\to m_2=1\\\\\text{Therefore}\ l:y=1x+b_2\to y=x+b_2\\\\\text{We know, the line}\ l\ \text{contains point (2, -2).}}\\\\\text{Substitute the coordinates to the equation of the line}\ l:\\\\-2=2+b_2\qquad|-2\\\\-4=b_2\to b_2=-4\\\\Answer:\ y=x-4`

Answer 2

Explanation:

Step One

Find the perpendicular to the line with a given slope of - 1

m1 * m2 = - 1 Let the given line have a slope of - 1. Call it m1

-1 * m2 = - 1 Divide both sides by -1

-1/-1 * m2 = -1/-1

m2 = 1

Step Two

Write what you have so far

y = 1 * x + b

y = x + b

Step Two

Solve the general equation for (2,-2)

y = x + b

x = 2

y = -2

-2 = 2 + b Subtract 2 from both sides

-2 - 2 = b switch and add

b= - 4

Answer

y = x -4