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

Answer:

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 = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

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

m = $\frac{6-1}{8-3}$ = $\frac{5}{5}$ = 1 ← slope of line a

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

m = $\frac{9-1}{2+6}$ = $\frac{8}{8}$ = 1 ← slope of line b

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