Question

What is the slope of a line that is perpendicular to the line whose equation is 0.5x−5y=9 0.5 x − 5 y = 9

Answer 1

i) one of the forms that we can write the equation of a line is 

y=mx+k

where m is the slope of the line.

ii)

given lines y=mx+k and y=nx+t, which are perpendicular to each other.

Then, m*n=-1


Now consider the line 0.5x−5y=9:

0.5x−5y=9

take -5y to the right side and 9 to the left side

0.5x-9=5y

switch sides

5y=0.5x-9

divide by 5

y=0.1x-9/5

so the slope of the line is m=0.1

let the slope of the line perpendicular to 0.5x−5y=9 be n, then

0.1*n=-1

n=-1/(0.1)=-10


Answer: -10