Answer:
[tex]y = 5\, x + 26[/tex].
Step-by-step explanation:
Start by finding the slope of the line perpendicular to [tex]y = (-1/5)\, x + 1[/tex].
The slope of [tex]y = (-1/5)\, x + 1[/tex] is [tex](-1/5)[/tex].
In a plane, if two lines are perpendicular to one another, the product of their slopes would be [tex](-1)[/tex].
Let [tex]m[/tex] denote the slope of the line perpendicular to [tex]y = (-1/5)\, x + 1[/tex]. The expression [tex](-1/5)\, m[/tex] would denote the product of the slopes of these two lines.
Since these two lines are perpendicular to one another, [tex](-1/5)\, m = -1[/tex]. Solve for [tex]m[/tex]: [tex]m = 5[/tex].
The [tex](-5,\, 1)[/tex] is a point on the requested line. (That is, [tex]x_{1} = -5[/tex] and [tex]y_{1} = 1[/tex].) The slope of that line is found to be [tex]m = 5[/tex]. The equation of that line in the point-slope form would be:
[tex]y - 1 = 5\, (x - (-5))[/tex].
Rewrite this point-slope form equation into the slope-intercept form:
[tex]y = 5\, x + 26[/tex].
