No, The lines y = –x – 4 and 5x + 5y = 20 are not perpendicular to each other. then lines are parallel to each other.
We have to determine, are the lines y = –x – 4 and 5x + 5y = 20 perpendicular.
To determine the given lines are perpendicular to each other following all the steps given below.
Equation of the lines; y = –x – 4 and 5x + 5y = 20
From line 2,
[tex]5x + 5y = 20[/tex]
Subtract 5x from each side,
[tex]5x - 5x + 5y = 20 - 5x\\\\5y = 20 - 5x[/tex]
Divide by 5 into both sides,
[tex]y = -x +4[/tex]
The slope of the line [tex]m_2 = -1[/tex]
From line 1,
[tex]y = -x -4[/tex]
The slope of the line [tex]m_ 1= -1[/tex].
The slope of given lines is perpendicular then the slope of the product of both lines is equal to -1.
Then,
[tex]=m_1 \times m_2\\\\ =-1 \times -1\\\\= 1[/tex]
Hence, No, The lines y = –x – 4 and 5x + 5y = 20 are not perpendicular to each other. the lines are parallel to each other.
To know more about Perpendicular lines click the link given below.
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