Need some help on equations (lines, spiral curves and polar curves)

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I have some issues with understanding the differences between implicit and explicit equations of lines and spirals. I have tried to do my assignment but found that I am struggling.

Here is my workings for Q1. The rest i'm still very unsure about how to approach it. Would appreciate help. I'm honestly not even sure if i am on the right track for the first question. Questions here

y-y1 = m(x-x1)

y-2=[(2-7)/(1-4)] (x-1)

y = 5x/3 + 1/3 and therefore, this is my parametric equation

x= u
y = 5u/3 + 1/3