Question

Find the equation of the line that passes through (3,2) and is perpendicular to y=3x-4

Answer 1

You are given a line (y=3x-4) and are asked to find the slope of a line perpendicular to the given line. How do you do that?

Answer 2

I don't know

Answer 3

I am trying to learn how

Answer 4

what's the slope of -> y=3x-4 ?

Answer 5

3

Answer 6

ok... so a line perpendicular to another line will have a NEGATIVE RECIPROCAL slope
so if y=3x-4 has a slope of 3
then the other line will have a slope of \(\bf {\color{blue}{ 3}}\qquad reciprocal\implies \cfrac{1}{{\color{blue}{ 3}}}\qquad negative\implies -\cfrac{1}{{\color{blue}{ 3}}}\)

so you're really being asked for
" Find the equation of the line that passes through (3,2) and has a slope of -1/3"

\(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 2}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= -\cfrac{1}{3}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form} \)