Find the slope of the line, computing it from any two points (X1, Y1) and (X2, Y2) on the line. The slope m = (Y1 - Y2) / (X1 - X2). Notice that it does not matter in which order you choose the points, because (Y1 - Y2) / (X1 - X2) = (Y2 - Y1) / (X2 - X1).
Find the slope intercept form using the slope and one point. The point-slope form is Y -Y1 = m(X - X1). If you know that the slope is 1/2 and the line goes through point (2, 3), the point-slope allows us to write: Y - 3 = 1/2(X - 2) or Y -3 = 1/2X - 1. This means that the slope intercept form is Y = 1/2X + 2.
Get the Y-axis intercept from the slope intercept form. If the slope intercept form is Y = mX + b, then b is the point where the line crosses the Y axis. Therefore, if the line that goes through the point (2, 3) and has slope 1/2 has the slope-intercept form Y = 1/2X + 2, then this line crosses the Y axis at the point (0, 2). A line with the formula Y = mX + b intercepts the Y axis at b.