Question

find the equation of a line that is perpendicular to the line 1/2x+2 and contains the points (5,0)

Answer 1

slope of a line perpendicular to a line with slope m
is
-1/m
so
slope is -2
y=-2x+c
c=10
y=-2x+10

Answer 2

Problem:
find the equation of a line that is perpendicular to the line 1/2x+2 and contains the points (5,0)

Here's how I would approach it.
When you have two perpendicular lines, if you take their two slopes and multiply them, you get -1.
So the line that is given has a slope of 1/2.
That means that the second line will have a slope of -2.
So, I can write the equation so far as: y = -2x + b
And b would be the y-intercept.
I would then substitute in x and y values for the point known to lie on the second line.
So I would have: 0 = -2(5) + b
I'd solve for b and find that b = 10
So the full equation is: y = -2x + 10

Hope that helps!