The line L1 has an equation y=2x-2. What is the equation of the line L2 which is parallel to L1 and passes through the point (0,3)?

The first thing to immediately recall is that parallel lines have the same gradient. in the equation of a line (which is expressed in the y=mx+c format), the gradient (m) is the coefficient of x.  Note: if the equation is expressed in a different format, it has to be brought back into the y=mx+c format, before the y-intercept or gradient can be determined. For example, if the equation is given is 4y-2x+3=0, then rearrange the equation so that 4y=2x-3, and then divide all the terms by the coeffiecient of y, so that we are left with y=0.5x-0.75. NOW, our gradient is the coefficient of x.  The gradient of L1 = gradient of L2 = 2 (Parallel lines) and we also know that L2 passes through the point (0,3) Substitute the following values into y=mx+c y=3 x=0 m=2 c=? and we get c=3, so the equation of L2 is: y=2x+3