Question

Determine which of the lines, if any, are parallel or perpendicular. Explain.

Line a: -x+2y=3

Line b: -6x=3y-1

Line c: 4x-8y=5

Answer 1

See below

Explanation:

Let's rewrite all three equations is standard slope-intercept format of y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0).

Line a: -x+2y=3

2y = x + 3

y = (1/2)x + 3

Line b: -6x=3y-1

-3y = 6x - 1

y = -2x + (1/3)

Line c: 4x-8y=5

-8y = -4x + 5

y = (1/2)x - (5/8)

Parallel lines have the same slope (m). Perpendicular lines have slopes that are the negative inverse (-1/m)of each other.

Slopes, m, for the lines are;

• a) (1/2)
• b) -2
• c) (1/2)

The negative inverse of (1/2) is -2.

Lines a and c are parallel (same slope)

Line b is perpendicular since it's slope is the negative inverse of both a and b (-1/(1/2)) = -2