Since Line J is perpendicular that means that it will be the negative inverse of -5, which is 1/5. So we have to input the point into the slope and do some thinking into what the y-int. will be. 1/5x5= 1. 1+8=9. The equation for Line J is y=1/5x+8
The line is 5y = x + 40.
A long thin scratch on the surface,
Given
[tex]m_{1} = -5 \\m_{2} = ?\\[/tex]
The line passes through (5,9)
We know the equation of a line.
[tex]y=m_{2} x+c[/tex]
But when the line is perpendicular then their slope product is -1.
[tex]\begin{aligned} m_{1} m_{2} &=-1\\m_{2} (-5) &=-1\\m_{2} &= \dfrac{1}{5} \\\end{aligned}[/tex]
Then
[tex]\begin{aligned} y &=\dfrac{1}{5} x+c\\5y &= x+c\\\end{aligned}[/tex]
This line passes through (5,9)
[tex]\begin{aligned} 5(9) &= 5 +c\\45 &=5+c\\c &= 40\\\end{aligned}[/tex]
Then, the line is 5y = x + 40.
More about the line link is given below.
https://brainly.com/question/14278862
