Tell whether the lines for each pair of equations are parallel, perpendicular, or neither: y=(−1/5)x+6,−2x+10y=5

Diego Barr

Diego Barr

Answered question

2022-10-31

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither: y = ( - 1 5 ) x + 6 , - 2 x + 10 y = 5

Answer & Explanation

Marlene Welch

Marlene Welch

Beginner2022-11-01Added 23 answers

Given -
y = ( - 1 5 ) x + 6 -------------------------(1)
- 2 x + 10 y = 5 ---------------------------(2)
The first line equation is in the slope intercept form
y=mx+c
The slope m1 of the 1st line is = - 1 5
The second line is in the form
ax+by=c
In this case, slope is defined by - a b
Applying this formula, the slope m 2 of the second line = - - 2 10 = 1 5
Then apply these conditions to decide the types of relation between the two lines.
If m 1 = m 2 , then the two lines are parallel to each other.
If the product of m 1 and m 2 is equal to −1 , then the two lines are perpendicular to each other.
Otherwise, the two lines are neither parallel nor perpendicular.
In our case m 1 = 1 5 and m 2 = 1 5 satisfy neither of the two conditions.
Hence they are neither parallel nor perpendicular.

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