To find the equation of the line in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) and the y-intercept \( b \).
Given the points \( (1, 3) \) and \( (0, -2) \):
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Calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's take \( (x_1, y_1) = (0, -2) \) and \( (x_2, y_2) = (1, 3) \): \[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]
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Identify the y-intercept \( b \): The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the point \( (0, -2) \), we see that \( b = -2 \).
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Write the equation: Substituting the values of \( m \) and \( b \) into the slope-intercept form gives us: \[ y = 5x - 2 \]
Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = 5x - 2} \]