Let's find the slope-intercept equation of this line. You can read off the y-intercept immediately; it's the place where x= 0 and the line crosses the y-axis. Here that intercept is b=-2.
The coordinates of that point are (0,-2).
Now let's find the slope of the line. Starting at (0,-2) move to the left 3 units (because -3 is the x-coordinate of the intersection of the line with the x-axis). From (0,-2), how far UP along the y-axis to the x-axis is it?
slope = rise / run. In this case, starting from (0,-2), and moving 3 units to the left, we get "run" = -3. Starting from (0,-2) and moving straight up to the x-axis, we get "rise" = 2.
The slope is then m = rise / run = 2/-3, or m = -2/3.
Thus, the equation of this line is y = mx + b, or y = (-2/3)x - 2.
