Greetings!
Convert the equation to slope y-intercept form:
[tex]-9y=-18x+28[/tex]
[tex] \frac{-9y}{-9}= \frac{-18x+28}{-9}[/tex]
[tex]y=2x-\frac{28}{9}[/tex]
The Slope of this equation is represented by 2 (or [tex] \frac{2}{1} [/tex]). In order to create a line perpendicular to this line, they must have negative reciprocals. The formula for this is: [tex](m_{1} )( m_{2})=-1[/tex] (m represents the slope each line).
Input the values we know:
[tex](2)( m_{2})=-1 [/tex]
Solve:
[tex]2m_{2}=-1 [/tex]
[tex]\frac{2m_{2}}{2}= \frac{-1}{2} [/tex]
[tex]m_{2}= \frac{-1}{2} [/tex]
Arrange the new equation in slope y-intercept form:
[tex]y= \frac{-1}{2}x+b [/tex]
Input a coordinate point into the equation:
[tex](6)= \frac{-1}{2}(-11)+b [/tex]
Solve
[tex](6)= \frac{11}{2}+b [/tex]
[tex] \frac{12}{2}= \frac{11}{2}+b[/tex]
[tex] \frac{12}{2}-\frac{11}{2}=b[/tex]
[tex] \frac{1}{2}=b[/tex]
The y-intercept is equal to [tex] \frac{1}{2}[/tex]
Now using the information we have, arrange the equation in slope y-intercept form:
[tex] \left[\begin{array}{ccc}y= \frac{-1}{2}x+ \frac{1}{2} \end{array}\right] [/tex]
Hope this helps!
-Benjamin
