To find the equation of the line in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and the point on the line.
Given:
- Slope \( m = \frac{2}{3} \)
- Point \( (-1, 3) \) where \( x = -1 \) and \( y = 3 \)
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Plug the point and slope into the point-slope formula: \[ y - y_1 = m(x - x_1) \] Substituting \( m = \frac{2}{3} \), \( x_1 = -1 \), and \( y_1 = 3 \): \[ y - 3 = \frac{2}{3}(x + 1) \]
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Distribute the slope: \[ y - 3 = \frac{2}{3}x + \frac{2}{3} \]
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Add 3 to both sides to solve for \( y \): \[ y = \frac{2}{3}x + \frac{2}{3} + 3 \]
Convert 3 to a fraction with a denominator of 3: \[ 3 = \frac{9}{3} \]
Now combine the fractions: \[ y = \frac{2}{3}x + \frac{2}{3} + \frac{9}{3} \] \[ y = \frac{2}{3}x + \frac{11}{3} \]
Thus, the equation of the line in slope-intercept form is: \[ y = \frac{2}{3}x + \frac{11}{3} \]