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Sagot :
to find a perpendicular line to another we need to know the slope of the first line, Fortunately we can find the slope with the two points
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where m is the slope (x2,y2) a point right from (x1,y1)
on this case (x2,y2)=(9,5) and (x1,y1)=(-3,9)
so replacing
[tex]\begin{gathered} m=\frac{5-9}{9-(-3)} \\ m=-\frac{1}{3} \end{gathered}[/tex]knowing the slope we can find the slope of the perpendicular and this is all than we need to make to lines paralels:
reverse slope and change the sign
so the slope of the new line is 3
[tex]-\frac{1}{3}\longrightarrow3[/tex]to write a equation we can use the general form
[tex]y=mx+b[/tex]where y is the solution, m the slope and x the variable and b it doesnt matter on this case because two lines are only made perpendicular by their slope, so you can use any number
like this
[tex]y=3x+1[/tex]that was the equation
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