First, let's find the slope (m) using the formula:
m = \frac{{y_2 - y_1}}{{x_2 - x_1}}
Given points (-2,0) and (0,3), we have:
m = \frac{{3 - 0}}{{0 - (-2)}} = \frac{3}{2}
Next, we can use the point-slope formula to find the equation of the line:
y - y_1 = m(x - x_1)
Using the point (-2,0) and the slope m = 3/2:
y - 0 = \frac{3}{2}(x - (-2))
y = \frac{3}{2}x + 3
Therefore, the equation of the line containing the points (-2,0) and (0,3) in slope-intercept form is:
\boxed{y = \frac{3}{2}x + 3}