what is the equation of the line through (4,2) and (0,-2) ?

Answer 1

To find the equation of the line that passes through the points \( (4, 2) \) and \( (0, -2) \), we can follow these steps:

1. Calculate the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) = (4, 2) \) and \( (x_2, y_2) = (0, -2) \).

   Substituting the values: \[ m = \frac{-2 - 2}{0 - 4} = \frac{-4}{-4} = 1 \]

2. Use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] We can use either of the two points. Using \( (4, 2) \): \[ y - 2 = 1(x - 4) \]

3. Simplifying the equation: \[ y - 2 = x - 4 \] \[ y = x - 2 \]

Therefore, the equation of the line that passes through the points \( (4, 2) \) and \( (0, -2) \) is: \[ y = x - 2 \]