Write the point-slope form of the line that passes through (5,5) and is perpendicular to a line with a slope of 1/4 include all of your work in your final answer.

Answer:The point-slope form of the line that passes through (5,5) and is perpendicular to a line with a slope of [tex]\frac{1}{4}[/tex] is 4x + y -25 = 0Solution:The point slope form of the line that passes through the points [tex]\left(x_{1} y_{1}\right)[/tex] and perpendicular to the line with a slope of “m” is given as  [tex]\bold{y-y_{1}=-\frac{1}{m}\left(x-x_{1}\right)}[/tex] ---- eqn 1Where “m” is the slope of the line. [tex]x_{1} \text { and } y_{1}[/tex] are the points that passes through the line.From question, given that slope “m” = [tex]\frac{1}{4}[/tex]Given that the line passes through the points (5,5).Hence we get[tex]x_{1}=5 ; y_{1}=5[/tex]By substituting the values in eqn 1 , we get the point slope form of the line which is perpendicular to the line having slope [tex]\frac{1}{4}[/tex]can be found out.y - 5 = -4(x - 5)y - 5 = -4x + 20on simplifying the above equation, we gety - 5 + 4x -20 = 04x + y - 25 = 0hence the point slope form of given line is 4x + y - 25 = 0