Question

State whether the lines are parallel, perpendicular, or neither. Show your work.
x–5y=103 and –2x=–206–10y.

Answer 1

Answer:

Neither

Explanation:

we know that

If two lines are parallel, then their slopes are the same and their y-intercept are different

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

we have

$x-5y=103$ ----> equation A

$-2x=-206-10y$ ----> equation B

step 1

Find the slope of line A

Isolate the variable y

$5y=x-103$

$y=\frac{1}{5}x-\frac{103}{5}$

the slope is equal to

$m_A=\frac{1}{5}$

step 2

Find the slope of line B

Isolate the variable y

$10y=2x-206$

$y=\frac{2}{10}x-\frac{206}{10}$

Simplify

$y=\frac{1}{5}x-\frac{103}{5}$

Compare

Line A and Line B are the same line

therefore

Neither