What is the equation of the line that passes through the points (6, 3) and (4, 9)?

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To find the equation of the line that passes through the points (6, 3) and (4, 9), we can follow these steps:

  1. Find the slope (m): The slope of a line passing through two points (x1, y1) and (x2, y2) is calculated with the formula:

    2. m = (y2 - y1) / (x2 - x1)

  2. Using the given points (6, 3) and (4, 9):
    Let (x1, y1) = (6, 3) and (x2, y2) = (4, 9).
    So, we have:

    3. m = (9 - 3) / (4 - 6)

    m = 6 / -2

    m = -3

  3. Use the point-slope form to find the equation: Now that we have the slope, we can use one of the points to find the equation of the line. The point-slope form of the equation is:

    4. y - y1 = m(x - x1)

  4. Using the point (6, 3):
    Plugging in the slope and the coordinates of the point provides:

    5. y - 3 = -3(x - 6)

  5. Now, distribute and simplify the equation:

    6. y - 3 = -3x + 18

    y = -3x + 18 + 3

    y = -3x + 21

  6. Final Equation: Therefore, the equation of the line that passes through the points (6, 3) and (4, 9) is:

    7. y = -3x + 21

This linear equation can effectively be used for further analysis or plotting on a graph. It indicates a downward slope, which confirms the line goes down as x increases, exactly as expected from the two given points.

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