To find the equation of the line in slope-intercept form \(y = mx + b\), we start by determining the slope \(m\) using the two points given: (0, -2) and (3, 0).
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Calculate the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{3 - 0} = \frac{0 + 2}{3} = \frac{2}{3} \]
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Use one point to solve for the y-intercept \(b\). We can use the point (0, -2): \[ y = mx + b \rightarrow -2 = \frac{2}{3}(0) + b \rightarrow -2 = b \]
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Now we have both \(m\) and \(b\):
- Slope \(m = \frac{2}{3}\)
- Y-intercept \(b = -2\)
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Write the equation in slope-intercept form: \[ y = \frac{2}{3}x - 2 \]
Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = \frac{2}{3}x - 2} \]