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Given the line y = − 2 5 x + 3, determine if the given line is parallel, perpendicular, or neither. Select the correct answer for each lettered part. A. y = 2 5 x + 7 A Parallel B Perpendicular C Neither B. 5y + 2x = −10 A Parallel B Perpendicular C Neither C. −5x + 2y = 4 A Parallel B Perpendicular C Neither

1 Answer

5 votes

Answer:

(a) Neither

(a) Perpemdicular

Explanation:

Required

Determine the relationship between given lines

(a)


y = -(2)/(5)x + 3

and


y = (2)/(5)x + 7

An equation written in form:
y=mx + b has the slope:


m \to slope

So, in both equations:


m_1 = -(2)/(5)


m_2 = (2)/(5)

For both lines to be parallel


m_1 = m_2

This is false in this case, because:


-(2)/(5) \\e (2)/(5)

For both lines to be perpendicular


m_1 * m_2 = -1

This is false in this case, because:


-(2)/(5) * (2)/(5) \\e -1

(b)


5y + 2x = -10

and


-5x + 2y = 4

Write equations in form:
y=mx + b


5y + 2x = -10


5y = -2x +10

Divide by 5


y = -(2)/(5)x +2


-5x + 2y = 4


2y = 5x + 4

Divide by 2


y = (5)/(2)x + 2

In both equations:


m_1 = -(2)/(5)


m_2 = (5)/(2)

For both lines to be parallel


m_1 = m_2

This is false in this case, because:


-(2)/(5) \\e (5)/(2)

For both lines to be perpendicular


m_1 * m_2 = -1

This is true in this case, because:


-(2)/(5) * (5)/(2) = -1

Cancel out 2 and 5


-1 = -1

User Robert Wills
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