Question

Determine from the given points of two lines if the lines are parallel, perpendicular, or neither. Enter your answers below. Use a forward slash (i.e. "/') for all fractions (e.g. 1/2 for 1/2 ). o Line a: (3,1) and (8,6) o Line b: (-6,1) and (2,9)​

Answer 1

lines are parallel

Step-by-step explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines is - 1

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = 3, 1) and (x₂, y₂ ) = (8, 6)

m =
`(6-1)/(8-3)` =
`(5)/(5)` = 1 ← slope of line a

Repeat with (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (2,9)

m =
`(9-1)/(2+6)` =
`(8)/(8)` = 1 ← slope of line b

Since both slopes are equal, line a and line b are parallel

Answer 2

The given lines are parallel because they both have slopes of 1.If they were perpendicular, their slopes would be negative reciprocals.

Step-by-step explanation:

To determine if two lines are parallel, perpendicular, or neither, we need to calculate their slopes. The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), often denoted as Δy/Δx which means 'change in y over change in x'.

For line a, the points are (3,1) and (8,6). So, the slope of line a, let's call it m1, is (6-1)/(8-3) = 5/5 = 1.

For line b, the points are (-6,1) and (2,9). So, the slope of line b, let's call it m2, is (9-1)/(2-(-6)) = 8/8 = 1.

Both lines have the same slope, which means they are parallel. If the lines were perpendicular, their slopes would be negative reciprocals (i.e., m1 = -1/m2).

Learn more about Slopes of Lines