Answer:
[tex]y=-\frac{1}{5} x-5[/tex]
Step-by-step explanation:
The given line is defined by: [tex]y=5x+1[/tex], where we see that the slope is 5 and the y-intercept 1.
In order to find a line perpendicular to the given one, we need it to have a slope that is the "opposite of the reciprocal" of the given slope.
"Opposite" means it would have its sign inverted (in our case from positive to negative); and "reciprocal means that instead of 5, it would be its reciprocal: [tex]\frac{1}{5}[/tex].
We can write this new line with such slope, and try to find its y-intercept (b) by using the given condition that requires it to go through the point (-5,-4) on he plane:
[tex]y=-\frac{1}{5} x+b[/tex]
we require then that when [tex]x=-5[/tex], the value of [tex]y=-4[/tex].
Therefore: [tex]-4=-\frac{1}{5} (-5)+b\\-4=\frac{5}{5} +b\\-4=1+b\\b=-4-1=-5[/tex]
Then our final answer is that the new line should have the form: [tex]y=-\frac{1}{5} x-5[/tex]
