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Using the graph, derive the equation of the line in slope-intercept form( 3,0) (0,-2)

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To derive the equation of the line in slope-intercept form \( y = mx + b \) using the points \( (3, 0) \) and \( (0, -2) \), follow these steps:

  1. Find the slope (m): The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

    Using the points \( (3, 0) \) and \( (0, -2) \):

    • Let \( (x_1, y_1) = (3, 0) \)
    • Let \( (x_2, y_2) = (0, -2) \)

    Now, calculate the slope: \[ m = \frac{-2 - 0}{0 - 3} = \frac{-2}{-3} = \frac{2}{3} \]

  2. Use the slope and one of the points to find the y-intercept (b): We can use the point \( (0, -2) \) since it directly gives us the y-intercept. The y-intercept \( b \) is the value of \( y \) when \( x = 0 \): \[ b = -2 \]

  3. Write the equation in slope-intercept form: Now that we have the slope \( m = \frac{2}{3} \) and the y-intercept \( b = -2 \), we can write the equation: \[ y = \frac{2}{3}x - 2 \]

Thus, the equation of the line in slope-intercept form is: \[ y = \frac{2}{3}x - 2 \]