Write the point-slope form of the line that passes through (5,5) and is parallel 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 parallel to a line with a slope of [tex]\frac{1}{4}[/tex] is x -4y +15 = 0 Solution: The point slope form of the line that passes through the points [tex]\left(x_{1} y_{1}\right)[/tex] and parallel to the line with slope “m” is given as  [tex]\bold{y-y_{1} = m\left(x-x_{1}\right)}[/tex] --- eqn 1 Where “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 parallel to the line having slope [tex]\frac{1}{4}[/tex] can be found out. [tex]y-5=\frac{1}{4}(x-5)[/tex]On cross multiplying we get 4y – 20 = x – 5 On rearranging, we get x-5-4y+20 = 0 x – 4y +15 = 0 hence the point slope form the given line is x – 4y +15 = 0