Answer:
the lines are perpendicular
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
x - 2y + 8 = 0 ( subtract x + 8 from both sides )
- 2y = - x - 8 ( divide all terms by - 2 )
y = [tex]\frac{1}{2}[/tex] x + 4 ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Given also
2x + y + 1 = 0 ( subtract 2x + 1 from both sides )
y = - 2x - 1 ← in slope- intercept form
with slope m = - 2
Parallel lines have equal slopes
The slopes are not equal thus the lines are not parallel.
For lines to be perpendicular the product of their slopes = - 1
[tex]\frac{1}{2}[/tex] × - 2 = -1
Thus the 2 lines are perpendicular.
