To find the equation of the line that passes through the points \((-3, 4)\) and \((-6, 3)\), we need to determine the slope and then use the point-slope form of a line.
- Calculate the slope (m):
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in our points:
- \((x_1, y_1) = (-3, 4)\)
- \((x_2, y_2) = (-6, 3)\)
\[ m = \frac{3 - 4}{-6 - (-3)} = \frac{-1}{-6 + 3} = \frac{-1}{-3} = \frac{1}{3} \]
- Use the point-slope form to find the equation:
The point-slope form of the equation of a line is given by:
\[ y - y_1 = m(x - x_1) \]
Using the slope \(m = \frac{1}{3}\) and the point \((-3, 4)\):
\[ y - 4 = \frac{1}{3}(x + 3) \]
- Convert to slope-intercept form (y = mx + b):
First, distribute on the right side:
\[ y - 4 = \frac{1}{3}x + 1 \]
Now, add 4 to both sides:
\[ y = \frac{1}{3}x + 1 + 4 \] \[ y = \frac{1}{3}x + 5 \]
So, the equation of the line in slope-intercept form is:
\[ \boxed{y = \frac{1}{3}x + 5} \]
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