write the point slope form of the line that passes through (5,5) and is parrallel to a line with a slope of 1/4. include all of your work in your final answer. type your answer in the box provided ?

Answer:[tex]4y-x = 15[/tex]       Step-by-step explanation:We are given the following information in the question:We have to find the equation of line passing through the point (5,5) anfd parallel to the line with slope [tex]\frac{1}{4}[/tex].Since the line is parallel, they will have the same slope.Thus, slope of line = [tex]\displaystyle\frac{1}{4}[/tex]Point-slope form:[tex](y-y_1) = m(x-x_1)[/tex],where m is the slope of line and [tex](x_1,y_1)[/tex] is a point on the line.Putting all the values, we have the equation of line:[tex](y-y_1) = m(x-x_1)\\(y-5) = \displaystyle\frac{1}{4}(x -5)\\\\4(y-5) = (x-5)\\4y-20 = x -5\\4y-x = -5+20\\4y-x = 15[/tex]The above equation is the required equation of the line.