Write the equation of a line perpendicular to y={1}{2}x+9 and through the point (5,0).

Answer 1

HI Kenny,

I am going to assume you mean y=1/2x +9 as your beginning equation.

To find the equation of a line perpendicular to the given one, you first need to find the slope. For perpendicular lines, you take the slope of the original (in this case, that would be 1/2) and flip it upside down and change the sign (opposite inverse). So, the slope of the new line would be -2.

Using the slope -2 and the point (5,0), we can substitute into the point-slope formula, which is y-y₁=m (x-x₁), so we have

y-0 =-2(x-5)

==>y= -2(x) - (-2)(5)

==> y=-2x+10. This would be the equation of the new line.