Answer:
![y = -\frac{3}{2}x+6](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%2B6)
Step-by-step explanation:
Given:
The given equation of the line
that passes through the point (4, 0).
Part A.
The equation of the line.
-----------(1)
Where:
m = Slope of the line
c = y-intercept
The given equation of the line.
![y = \frac{2}{3} x + 5](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20x%20%2B%205)
Comparing the given equation with equation 1.
The slope of the line is
and y-intercept ![c = 5](https://tex.z-dn.net/?f=c%20%3D%205)
We know that the slope of the perpendicular line is
.
So the slope of the perpendicular line is
.
Using point slope formula we write the equation of the perpendicular line that passes through the point (4, 0).
![y-y_{1} = m(x-x_{1}](https://tex.z-dn.net/?f=y-y_%7B1%7D%20%3D%20m%28x-x_%7B1%7D)
Now we substitute the slope of the perpendicular line
and
from point (4, 0) in above equation.
![y-0 = -\frac{3}{2}(x-4)](https://tex.z-dn.net/?f=y-0%20%3D%20-%5Cfrac%7B3%7D%7B2%7D%28x-4%29)
![y = -\frac{3}{2}x-(-\frac{3}{2}\times 4)](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx-%28-%5Cfrac%7B3%7D%7B2%7D%5Ctimes%204%29)
![y = -\frac{3}{2}x-(-3\times 2)](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx-%28-3%5Ctimes%202%29)
![y = -\frac{3}{2}x-(-6)](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx-%28-6%29)
![y = -\frac{3}{2}x+6](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B2%7Dx%2B6)
Therefore the perpendicular line equation is
.
Part B.
1. The slope of the perpendicular line is
.
2. The y-intercept of the perpendicular line is 6.
3. The equation of the line
is perpendicular to the equation of line
.