Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through
the point (6, 3).
We need to find the slope of the perpendicular line. Then we can find an equation for the line
using point-slope form.
The original equation y = 2x + 2 is in slope-intercept form (y=mx+b) so we can read the slope
right off the equation. The slope m is 2.
The slope of the perpendicular line will always have the slope -1/m. In this case, the slope of
the perpendicular line is -1/m=-1/2.
The point-slope form for a line is y-y = m(x-x), where m is the slope and (x,y) is a point on the line.
The point (x,y) is (6,3), so the equation is
y - (3) = (-1/2)(x - 6)
You can simplify this a bit if we want to, but it's not essential.
y-3 = (-1/2)x+3
y = (-1/2)x+6
Feel free to email if you have questions about the solution.