Question

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:
\[
y = x - 2
\]