Question

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

Answer 1

(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`