Answer:
Slope of perpendicular line: 5
Slope of parallel line: -1/5
Explanation:
Convert the equation to slope-intercept form (y=mx+b where m is the slope and b is the y-intercept)
x+5y=6
subtract x on both sides
5y=-x+6
divide by 5 on both sides
y=-(1/5)x+6/5
The slope of this equation is the coefficient of x, -1/5.
The slopes of two perpendicular lines are negative reciprocals of each other.
To get the negative reciprocal of a number, flip the numerator and denominator and multiply by -1.
-1/5 becomes 5, so that's the slope of a line perpendicular to our original line.
Parallel lines have the same slope, so that's just -1/5.
Slope of perpendicular line: 5
Slope of parallel line: -1/5