Question

The equation of line r is y = -1\2x - 4. If line s runs perpendicular to line r and passes through (4, -3), what would be the equation of line s?

Answer 1

first off, what's the slope of "r" anyway,
`\bf y=\stackrel{slope}{-\cfrac{1}{2}}x-4`.

low and behold, since "r" is in slope-intercept form, notice, it has a slope of -1/2.

now, any line perpendicular to "r", will have a negative reciprocal slope to it, that is,


`\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{2}\\\\ negative\implies +\cfrac{1}{{{ 2}}}\qquad reciprocal\implies + \cfrac{{{ 2}}}{1}\implies 2`

so we're really looking for a line whose slope is 2, and runs through 4,-3,