Answer:
The equation in slope-intercept form for the path of the trumpet players is
.
Step-by-step explanation:
Consider the provided information.
The drummers will march along the line y=-5x-8.
The trumpets players will march along a perpendicular line that passes through (-2,2).
The slope of line y=-5x-8 is: m₁ = -5.
The slope of perpendicular lines are: ![m_1\times m_2=-1](https://tex.z-dn.net/?f=m_1%5Ctimes%20m_2%3D-1)
![-5\times m_2=-1](https://tex.z-dn.net/?f=-5%5Ctimes%20m_2%3D-1)
![m_2=\frac{1}{5}](https://tex.z-dn.net/?f=m_2%3D%5Cfrac%7B1%7D%7B5%7D)
Hence, the slope of the line should be 1/5.
The line passes through (-2,2).
Now use point slope form to find the equation of line.
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Substitute m=1/5, x₁=-2 and y₁ = 2 in above formula.
![y-2=\frac{1}{5}(x+2)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B1%7D%7B5%7D%28x%2B2%29)
![y-2=\frac{x}{5}+\frac{2}{5}](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7Bx%7D%7B5%7D%2B%5Cfrac%7B2%7D%7B5%7D)
![y=\frac{x}{5}+\frac{2}{5}+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7B5%7D%2B%5Cfrac%7B2%7D%7B5%7D%2B2)
![y=\frac{x}{5}+\frac{12}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7B5%7D%2B%5Cfrac%7B12%7D%7B5%7D)
Hence, the equation in slope-intercept form for the path of the trumpet players is
.