Answer:
y = -5x -17
Explanation:
We were given the information:
[tex]\begin{gathered} x-5y=2 \\ (-4,3) \end{gathered}[/tex]
We will proceed to obtain the equation for the line:
[tex]\begin{gathered} x-5y=2 \\ \text{Subtract ''x'' from both sides, we have:} \\ -5y=2-x \\ \text{Divide both sides by ''-5'', we have:} \\ y=-\frac{2}{5}-\frac{1}{-5}x \\ y=-\frac{2}{5}+\frac{1}{5}x \\ y=\frac{1}{5}x-\frac{2}{5} \\ \text{Comparing with the standard form, }y=mx+b,\text{ we have:} \\ mx=\frac{1}{5}x \\ slope(m)=\frac{1}{5} \end{gathered}[/tex]
We will proceed as follows:
[tex]\begin{gathered} \text{For a perpendicula}r\text{ line, the slope is given by:} \\ m_{perpendicular}=-\frac{1}{m} \\ m_{perpendicular}=-\frac{1}{\frac{1}{5}} \\ m_{perpendicular}=-5 \\ \text{The perpendicular line lies on the point (-4, 3). Using the point-slope equation, we have:} \\ y-y_1=m_{}(x-x_1)\Rightarrow y-y_1=m_{perpendicular}(x-x_1) \\ (x_1,y_1)=(-4,3) \\ y-3=-5(x--4) \\ y-3=-5(x+4) \\ y-3=-5x-20 \\ \text{Add ''3'' to both sides, we have:} \\ y=-5x-20+3 \\ y=-5x-17 \\ \\ \therefore y=-5x-17 \end{gathered}[/tex]
Therefore, the equation of the perpendicular line to that equation that lies on the point (-4, 3) is: y = -5x -17
