To derive the equation of the line in slope-intercept form (y = mx + b) using the points (0, 3) and (3, 2), we first need to determine the slope (m) of the line.
The slope (m) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where (x₁, y₁) = (0, 3) and (x₂, y₂) = (3, 2).
Substituting the values into the formula: \[ m = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \]
Now that we have the slope, we can use one of the points to find the y-intercept (b). The point (0, 3) indicates that when x = 0, y = 3, which means the y-intercept (b) is 3.
Now we have:
- Slope (m) = -\(\frac{1}{3}\)
- Y-intercept (b) = 3
We can now write the equation of the line in slope-intercept form: \[ y = -\frac{1}{3}x + 3 \]
Therefore, the equation of the line in slope-intercept form is: \[ y = -\frac{1}{3}x + 3 \]
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