Glencoe Algebra 2, Chapter 2, 2.4, Section 2.4, Problem 10

Given
the line is y= x-2 and the slope of the line is m_1 = 1
as we know that the product of the slopes of the two perpendicular lines is equal to -1
let the slope of the required line is m_2
so ,
(m_1)(m_2) = -1
=> m_2 = -1 as m_1 = 1
and the required line passes through (0, -2)

and slope m_2= -1
As,the slope-intercept form of a line is
y= mx+b
from the above we know m_2 = -1 , so the line equation is
y= (-1)x+b --------------(1)
we need to find the value of b , as the line passes through the point
(x,y)= (0, -2 ) , then on substituting we get
0 =(-1)*(-2)+b
=> b = -2
so the equation of the line is
y= (-1)x-2