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=(-3-2)/(0-(-2))=-(5)/(2)`

so, the slope of the perpendicular line is

`-(5)/(2)\longrightarrow(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=(2)/(5)x+b \\ 1=(2)/(5)(10)+b \\ b=1-(2)/(5)(10) \\ \\ b=-3 \end{gathered}`

so the equation of the perpendicular line is

`y=(2)/(5)x-3`