To find the equation of the line that passes through the points \((-3, 4)\) and \((-6, 3)\), we first need to calculate the slope of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let \((x_1, y_1) = (-3, 4)\) and \((x_2, y_2) = (-6, 3)\). Plugging in these values:
\[ m = \frac{3 - 4}{-6 - (-3)} = \frac{-1}{-6 + 3} = \frac{-1}{-3} = \frac{1}{3} \]
Now we have the slope \(m = \frac{1}{3}\).
Next, we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
Using one of the points, say \((-3, 4)\), we can substitute in the values:
\[ y - 4 = \frac{1}{3}(x + 3) \]
Now we will simplify this equation:
\[ y - 4 = \frac{1}{3}x + 1 \]
Adding 4 to both sides:
\[ y = \frac{1}{3}x + 1 + 4 \] \[ y = \frac{1}{3}x + 5 \]
Thus, in slope-intercept form \(y = mx + b\), the equation of the line is:
\[ y = \frac{1}{3}x + 5 \]
So, your answer is:
\[ y = \frac{1}{3}x + 5 \]