Question

Which equation represents the graph?

a graph of a line that passes through the points 0 comma negative 2 and negative 2 comma 2

Answer 1

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

1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's assign:
- \((x_1, y_1) = (0, -2)\)
- \((x_2, y_2) = (-2, 2)\)

Now substitute the values:
\[
m = \frac{2 - (-2)}{-2 - 0} = \frac{2 + 2}{-2} = \frac{4}{-2} = -2
\]

2. **Use the point-slope form of the equation of a line**, which is:
\[
y - y_1 = m(x - x_1)
\]

Using the point \((0, -2)\) and the slope \(m = -2\):
\[
y - (-2) = -2(x - 0)
\]
This simplifies to:
\[
y + 2 = -2x
\]
Subtracting 2 from both sides gives:
\[
y = -2x - 2
\]

Thus, the equation that represents the graph of the line passing through the points \((0, -2)\) and \((-2, 2)\) is:
\[
\boxed{y = -2x - 2}
\]