Question 530904
First you have to figure out the slope of the line given, because parallel lines have the same slope.
The slope of the line
{{{y=2x-3}}}
is 2 because every time x increases by 1, y increases by 2, and for any other increase in x, y will increase by 2 times as much.
When a line is given in the form
{{{y=mx+b}}} with {{{m}}} and {{{b}}} being two numbers, positive or negative,
the number multiplying the x (in your case {{{m=2}}}) is the slope.
The y-intercept, some times called intercept, is the b number.
In the case of the given line, {{{b=-3}}}, but that does not matter for the problem.
The intercept (y-intercept) is the point where the line intercepts the y-axis, which is the line {{{x=0}}}.
The y-intercept point will be (x,b). (The x value will always be zero).
If you have the slope of a line ({{{m}}})
and the y value for the intercept ({{{b}}})
you can write the equation of the line as {{{y=mx+b}}}.
The parallel line you need has the same slope as the line given: {{{m=2}}}.
The y-intercept point (0,6) has {{{y=6}}}, so you use {{{b=6}}}
Your line is {{{y=2x+6}}}