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

Answer:

(a) Neither

(a) Perpemdicular

Step-by-step explanation:

Required

Determine the relationship between given lines

(a)

$y = -\frac{2}{5}x + 3$

and

$y = \frac{2}{5}x + 7$

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

$m \to slope$

So, in both equations:

$m_1 = -\frac{2}{5}$

$m_2 = \frac{2}{5}$

For both lines to be parallel

$m_1 = m_2$

This is false in this case, because:

$-\frac{2}{5} \ne \frac{2}{5}$

For both lines to be perpendicular

$m_1 * m_2 = -1$

This is false in this case, because:

$-\frac{2}{5} * \frac{2}{5} \ne -1$

(b)

$5y + 2x = -10$

and

$-5x + 2y = 4$

Write equations in form: $y=mx + b$

$5y + 2x = -10$

$5y = -2x +10$

Divide by 5

$y = -\frac{2}{5}x +2$

$-5x + 2y = 4$

$2y = 5x + 4$

Divide by 2

$y = \frac{5}{2}x + 2$

In both equations:

$m_1 = -\frac{2}{5}$

$m_2 = \frac{5}{2}$

For both lines to be parallel

$m_1 = m_2$

This is false in this case, because:

$-\frac{2}{5} \ne \frac{5}{2}$

For both lines to be perpendicular

$m_1 * m_2 = -1$

This is true in this case, because:

$-\frac{2}{5} * \frac{5}{2} = -1$

Cancel out 2 and 5

$-1 = -1$