Answer:
[tex]y=5x-23[/tex]
Step-by-step explanation:
step 1
Find the slope of the line that is perpendicular to the given line
we have
[tex]y=-\frac{1}{5}x+3[/tex] -----> given line
The slope of the given line is
[tex]m=-\frac{1}{5}[/tex]
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal
therefore
The slope of the line that is perpendicular to the given line is
[tex]m=5[/tex]
step 2
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=5\\point\ (4,-3)[/tex]
substitute
[tex]-3=5(4)+b[/tex]
solve for b
[tex]b=-23[/tex]
therefore
[tex]y=5x-23[/tex]
