Respuesta :
Given the equation:
[tex]y+5x=7[/tex]we can find its slope if we write it in the y=mx+b form:
[tex]\begin{gathered} y+5x=7 \\ \Rightarrow y=-5x+7 \end{gathered}[/tex]Now, we know as a general rule, that the slope of the perpendicular of the line that has slope m, is -1/m, more clearly:
[tex]\begin{gathered} \text{if m is the slope of the line} \\ \Rightarrow m_p=-\frac{1}{m}\text{ is the slope of the perpendicular line} \end{gathered}[/tex]So, in this case we have:
[tex]\begin{gathered} m=-5 \\ \Rightarrow m_p=-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5} \\ m_p=\frac{1}{5} \end{gathered}[/tex]now we use the slope-point formula to find the equation of the perpendicular line:
[tex]\begin{gathered} (x_0,y_0)=(10,-4) \\ m_p=\frac{1}{5}_{} \\ y-y_0=m(x-x_0)_{} \\ \Rightarrow y-(-4)=\frac{1}{5}(x-10) \\ \Rightarrow y+4=\frac{1}{5}x-\frac{10}{5} \\ \Rightarrow y=\frac{1}{5}x-2-4=\frac{1}{5}x-6 \\ y=\frac{1}{5}x-6 \end{gathered}[/tex]therefore, the line perpendicular to y+5x=7 that passes through (10,-4) is y=1/5x-6
