Answer:
Equation of the perpendicular line is [tex]y=-\frac{1}{5}x+1[/tex]
Step-by-step explanation:
Given equation is y = 5x - 4
By comparing this equation with slope-intercept form of the equation,
y = mx + b
Slope of this line [tex]m_{1}=5[/tex]
Let the slope of the perpendicular line = [tex]m_{2}[/tex]
By the property of perpendicular lines,
[tex]m_{1}\times m_{2}=(-1)[/tex]
[tex]5\times m_{2}=(-1)[/tex]
[tex]m_{2}=-\frac{1}{5}[/tex]
Equation of the perpendicular line passing through a point [tex](x_{1}, y_{1})[/tex] and slope m is represented by
[tex]y-y_{1}=m(x-x_{1})[/tex]
If the given point is (10, -1) and slope 'm'= [tex]-\frac{1}{5}[/tex]
[tex]y+1=-\frac{1}{5}(x-10)[/tex]
[tex]y=-\frac{1}{5}x+2-1[/tex]
[tex]y=-\frac{1}{5}x+1[/tex]
