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,
\(5x + 5y = 20\)
Subtract 5x from each side,
\(5x - 5x + 5y = 20 - 5x\\\\5y = 20 - 5x\)
Divide by 5 into both sides,
\(y = -x +4\)
The slope of the line \(m_2 = -1\)
From line 1,
\(y = -x -4\)
The slope of the line \(m_ 1= -1\).
The slope of given lines is perpendicular then the slope of the product of both lines is equal to -1.
Then,
\(=m_1 \times m_2\\\\ =-1 \times -1\\\\= 1\)
Hence, No, The lines y = –x – 4 and 5x + 5y = 20 are not perpendicular to each other. the lines are parallel to each other.
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