Respuesta :
Given:
The given equation is:
[tex]y=-4x+3[/tex]
A line is perpendicular to the given line and passes through the point (4,-1).
To find:
The equation of required line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
We have,
[tex]y=-4x+3[/tex]
Here, the slope of the line is -4 and the y-intercept is 3.
Let the slope of required line be m.
We know that the product of slopes of two perpendicular lines is -1. So,
[tex]m\times (-4)=-1[/tex]
[tex]m=\dfrac{-1}{-4}[/tex]
[tex]m=\dfrac{1}{4}[/tex]
The slope of required line is [tex]m=\dfrac{1}{4}[/tex] and it passes through the point (4,-1). So, the equation of the line is:
[tex]y-(-1)=\dfrac{1}{4}(x-4)[/tex]
[tex]y+1=\dfrac{1}{4}(x)-\dfrac{4}{4}[/tex]
[tex]y=\dfrac{1}{4}x-1-1[/tex]
[tex]y=\dfrac{1}{4}x-2[/tex]
Therefore, the equation of the required line is [tex]y=\dfrac{1}{4}x-2[/tex].
