Answer:
The required equation of the line is:
[tex]y=\frac{1}{4}x-1[/tex]
Step-by-step explanation:
Given the equation
[tex]y=-4x+3[/tex]
comparing the equation with the slope-intercept form
[tex]y=mx+b[/tex]
Here,
so the slope of the line is -4.
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be: 1/4
Therefore, the point-slope form of the equation of the perpendicular line that also intersects the point (8, 1) is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-1=\frac{1}{4}\left(x-8\right)[/tex]
add 1 to both sides
[tex]y-1+1=\frac{1}{4}\left(x-8\right)+1[/tex]
[tex]y=\frac{1}{4}x-1[/tex]
