Question

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

Answer 1

For lines to be perpendicular to one another the product of their slopes must be negative one.  Or in other words their slopes must be negative reciprocals of one another.  Mathematically this is:

m1*m2=-1, in this case our reference lines is:

0.5x-5y=9

5y=0.5x-9

y=0.1x-1.8 so its slope is 0.1, so the perpendicular slope, m, is:

0.1m=-1

m=-10

So the slope of the line perpendicular to 0.5x-5y=9 is -10.

Answer 2

Make equation y intercept form so you can know the slope.of that equation (the slope is the number before the x)
.5x-5y=9
-.5x both sides
-5y=-.5x+9
÷-5 both sides
Y=.1x-9/5
Slope is .1 or 1/10
To have a slope of a perpendicular line you flip the fraction and chance signs
The perpendicular lines slope is -10