``passes through (0, -2), perpendicular to the graph of y = x - 2`` Write an equation in slope-intercept form for the line that satisfies each set of conditions.

Textbook Question

Chapter 2, 2.4 - Problem 10 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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kspcr111 | In Training Educator

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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`

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