Question

What line is perpendicular to y=1/3+2 and passes through (6,-3)

Answer 1

keeping in mind that perpendicular lines have negative reciprocal slopes, hmmm so, what is the slope of y = 1/3x + 2 anyway? well


`\bf y=\stackrel{slope}{\cfrac{1}{3}}x+2\qquad therefore \\\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{1}}\implies -3}`

so, we're really looking for the equation of a line whose slope is -3 and runs through 6, -3.


`\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{-3})\qquad \qquad \qquad slope = m\implies -3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=-3(x-6) \\\\\\ y+3=-3x+18\implies y=-3x+15`