The equation of a line:
[tex]y=mx+b[/tex]
m - the slope, b - the y-intercept
The y-intercept of the first line is -6.
[tex]y=m_1x-6[/tex]
It passes through (x,y)=(-2,4). Plug the values into the equation and calculate m:
[tex]4=m_1 \times (-2)-6 \\
4+6=-2m_1 \\
10=-2m_1 \\
\frac{10}{-2}=m_1 \\
m_1=-5[/tex]
The slope of the first line is -5.
The product of the slopes of two perpendicular lines is -1.
[tex]m_1 \times m_2=-1 \\ -5 \times m_2=-1 \\
m_2=\frac{-1}{-5} \\
m_2=\frac{1}{5}[/tex]
The slope of the second line is 1/5.
[tex]y=\frac{1}{5}x+b[/tex]
It passes through (x,y)=(5,-4). Plug the values into the equation and calculate b:
[tex]-4=\frac{1}{5} \times 5+b \\
-4=1+b \\
-4-1=b \\
b=-5 \\ \\
\boxed{y=\frac{1}{5}x-5}[/tex]
