Respuesta :
We need to determine the equation of the line in point-slope form, which is shown below:
[tex]y-y_0=m\cdot(x-x_0)[/tex]Where (x0, y0) is a point that belongs to the line, and m is the slope.
The first step we need to take, is to determine the slope of the line given to us, which is done below:
[tex]\begin{gathered} 4x-6y=24 \\ -6y=24-4x \\ y=\frac{4}{6}x-4 \end{gathered}[/tex]The slope for this line is 4/6. We want to determine the line that is perpendicular to it, which means we have to find the slope the negative reciprocal to this slope, which is done below:
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{\frac{4}{6}} \\ m_2=-\frac{6}{4} \\ m_2=\frac{-3}{2} \end{gathered}[/tex]The slope of the perpendicular line is -3/2. The point we need is (-2, 5), therefore the equation is:
y-5=-1.5*(x- (-2) )
