To derive the equation of the line in slope-intercept form (y = mx + b) using the points (1, 3) and (0, -2), follow these steps:
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Determine the slope (m): The formula for slope (m) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (1, 3) and (0, -2): \[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]
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Use the point (0, -2) to find the y-intercept (b): In slope-intercept form, the y-intercept is the value of y when x = 0. The point (0, -2) indicates that when x is 0, y is -2. Thus, b = -2.
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Write the equation in slope-intercept form: Now we can substitute m and b into the slope-intercept form. \[ y = mx + b \implies y = 5x - 2 \]
Thus, the equation of the line in slope-intercept form is: \[ y = 5x - 2 \]