To find the equation of the line that passes through the points \((-3, 4)\) and \((-6, 3)\), we first need to determine the slope \(m\) of the line using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Taking the points \((-3, 4)\) as \((x_1, y_1)\) and \((-6, 3)\) as \((x_2, y_2)\):
\[ m = \frac{3 - 4}{-6 - (-3)} = \frac{-1}{-6 + 3} = \frac{-1}{-3} = \frac{1}{3} \]
Now that we have the slope \(m = \frac{1}{3}\), we can use the point-slope form of the line equation, which is:
\[ y - y_1 = m(x - x_1) \]
We can use either point, but let's use the point \((-3, 4)\):
\[ y - 4 = \frac{1}{3}(x + 3) \]
Now, we can simplify this equation:
\[ y - 4 = \frac{1}{3}x + 1 \]
Next, isolate \(y\) by adding 4 to both sides:
\[ y = \frac{1}{3}x + 1 + 4 \]
\[ y = \frac{1}{3}x + 5 \]
Thus, the equation of the line in slope-intercept form is:
\[ \boxed{y = \frac{1}{3}x + 5} \]