Question 100359
Parallel lines have the same slope (by definition), so the slope of the line passing through the point(-2,1) will have to have slope = -2/3. We know that the line is sloping down to the right because the slope is negative. The slope is also the change in y divided by the change in x, so for each change of 3 on the x-axis, the y value decreases by 2 (that is, -2/3). To define a line, we need another point to pair with (-2,1).

We know that the general equation for a line is {{{y = mx + b}}}. We know one y and one x, but we don't know b, so we substitute what we know and solve that.

{{{1 = (-2/3) * -2 + b}}}

{{{1 = 4/3 + b}}} so {{{b = -1/3}}}

Recall the b is called the y-intercept, which tells us where the line crosses the y-axis when x=0.  That gives us another coordinate pair:  (0, -1/3). So the equation for the line is: 

{{{y = (-2/3)x - 1/3}}}.