Question

what is the equation that is perpendicular to y=-3/2x+4 AND that passes through the points (3,9) and how do you get it?

Answer 1

so...what do you think is the slope of => y=-3/2x+4 ?

Answer 2

-1.5

Answer 3

well... -3/2 yes or -1.5

so a line perpendicular to that one, will have a NEGATIVE RECIPROCAL slope to that one
meaning \(\bf -\cfrac{3}{2}\qquad negative\to +\cfrac{3}{2}\qquad reciprocal\to +\cfrac{2}{3}\)

so you're really being asked to find the equation of a line whose slope is \(\frac{2}{3}\) and that passes through (3,9)

so \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 9}})\quad
\end{array}
\\\quad \\

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

Answer 4

oh okay! thanks that helps