Question

Line L has equation 2x - 3y = 5.
Line M passes through the point (2, -10) and is perpendicular to line L.
Determine the equation for line M.

Answer 1

can you solve -> 2x - 3y = 5. <- for "y" ? what would that give you?

Answer 2

y=2x/3−5/3

Answer 3

so....notice the slope of that line \(\bf y={\color{blue}{ \cfrac{2}{3}}}x-\cfrac{5}{3}\) thus is 2/3

well, the slope of a line that is perpendicular to the line of that equation will have a NEGATIVE RECIPROCAL slope
that is \(\bf {\color{blue}{ \cfrac{2}{3}}}\qquad reciprocal \implies {\color{blue}{ \cfrac{3}{2}}}\qquad negative\implies -{\color{blue}{ \cfrac{3}{2}}}\)

so the equation for line M will be the equation of a line that passes through (2, -10) and has a slope of -3/2 thus \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 2}}\quad ,&{\color{blue}{ -10}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= -\cfrac{3}{2}
\\ \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}\)