To find the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope (m) between the two points (3, 0) and (0, -2).
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Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, (x1, y1) = (3, 0) and (x2, y2) = (0, -2).
\[ m = \frac{-2 - 0}{0 - 3} = \frac{-2}{-3} = \frac{2}{3} \]
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Use the slope and one of the points to find the y-intercept (b). We can use the point (3, 0): \[ y = mx + b \] Plugging in the values: \[ 0 = \frac{2}{3}(3) + b \] \[ 0 = 2 + b \] \[ b = -2 \]
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Now write the equation in slope-intercept form: \[ y = \frac{2}{3}x - 2 \]
Thus, the equation of the line in slope-intercept form is: \[ y = \frac{2}{3}x - 2 \]
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