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An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.

Write the equation of the line in slope-intercept form.

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1 answer

To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) of the line and the y-intercept (b).

  1. Calculate the slope (m): The slope (m) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \( (0, -2) \) and \( (3, 0) \):

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

    Plugging in the values: \[ m = \frac{0 - (-2)}{3 - 0} = \frac{2}{3} \]

  2. Find the y-intercept (b): The y-intercept is the value of y when x = 0. From the point (0, -2), we can see that: \[ b = -2 \]

  3. Write the equation: Now we can use the slope and y-intercept to write the equation of the line: \[ y = \frac{2}{3}x - 2 \]

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