through: (4,4) and (2,-4)

1 answer

It looks like you're looking for the equation of the line that passes through the points (4, 4) and (2, -4). Here's how you can find it:

  1. Calculate the slope (m): The slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

    \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

    Substituting the points (4, 4) and (2, -4):

    \[ m = \frac{-4 - 4}{2 - 4} = \frac{-8}{-2} = 4 \]

  2. Use the point-slope form of the equation of a line: Once you have the slope, you can use the point-slope form of a line's equation, which is:

    \[ y - y_1 = m(x - x_1) \]

    We can use either of the two points. Let's use (4, 4):

    \[ y - 4 = 4(x - 4) \]

    Simplifying this:

    \[ y - 4 = 4x - 16 \]

    \[ y = 4x - 12 \]

  3. Final Equation: Therefore, the equation of the line passing through the points (4, 4) and (2, -4) is:

    \[ y = 4x - 12 \]

If you require further transformations or specific forms, feel free to ask!