Answer:
y-intercept is 4.
Step-by-step explanation:
Given,
Equation of the line,
![y=\frac{4}{3}x+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B3%7Dx%2B1)
∵ Equation of a line is y = mx + c, where m is the slope of the line,
By comparing,
The slope of the above line is
,
Let m' is the slope of the line perpendicular to above line,
![\implies m'\times \frac{4}{3}=-1](https://tex.z-dn.net/?f=%5Cimplies%20m%27%5Ctimes%20%5Cfrac%7B4%7D%7B3%7D%3D-1)
![\implies m' = -\frac{3}{4}](https://tex.z-dn.net/?f=%5Cimplies%20m%27%20%3D%20-%5Cfrac%7B3%7D%7B4%7D)
Now, the equation of a line passes through a point
is,
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
So, the equation of the perpendicular line having slope
and passes through ( 4,1) is,
![y-1=-\frac{3}{4}(x-4)\implies y=-\frac{3}{4}x+3+1\implies y=-\frac{3}{4}x+4](https://tex.z-dn.net/?f=y-1%3D-%5Cfrac%7B3%7D%7B4%7D%28x-4%29%5Cimplies%20y%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B3%2B1%5Cimplies%20y%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B4)
For y-intercept,
x = 0,
⇒ y = 4
Hence, the y-intercept of the perpendicular line is 4.