Question

Write the equation of the line that is perpendicular to the line mand passing through the point (10,1).

Answer 1

when 2 lines are perpendicular the slopes are inverted and have a different sign

for example if a slope is 2, the slope of perpendicular line is -1/2

take two poins of m line (-2,2) and (0,-3)

the slope of the m line is

$m=\frac{-3-2}{0-(-2)}=-\frac{5}{2}$

so, the slope of the perpendicular line is

$-\frac{5}{2}\longrightarrow\frac{2}{5}$

now, the geberal form of the line is

$y=mx+b$

where m is the slope and b the y-intercept

we replace the slope= 1/5 and repace the point (10,1) to find b

$\begin{gathered} y=\frac{2}{5}x+b \\ 1=\frac{2}{5}(10)+b \\ b=1-\frac{2}{5}(10) \\ \\ b=-3 \end{gathered}$

so the equation of the perpendicular line is

$y=\frac{2}{5}x-3$