We are given the line of equation 2x+y = 3 and told to find the slope of the line that is parallel to this line. REcall that two lines are parallel if and only if they have the same slope. So, what the question is really asking is to find the slope of this line. REcall that the general equation of a line, in slope-intercept form is
where m is the slope and b is the y -intercept. So, the idea is to take the original equation and put it in slope - intercept form.
We start with
If we subtract 2x on both sides, we get
which is the slope - intercept form of the line. We can see that in here m has the value of -2. So the slope of this line is -2. Hence, any line that is parallel to this line has also a slope of -2.