Question

Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.

Answer 1

To analyze the line passing through the points \((-2, 0)\) and \((2, -4)\), we can determine its slope, equation, and intercepts.

1. **Calculate the slope (m)**:
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (-2, 0)\) and \((x_2, y_2) = (2, -4)\):
\[
m = \frac{-4 - (0)}{2 - (-2)} = \frac{-4}{4} = -1
\]

2. **Equation of the line**:
We can use point-slope form \(y - y_1 = m(x - x_1)\) with the point \((-2, 0)\):
\[
y - 0 = -1(x - (-2)) \\
y = -x - 2
\]

3. **Y-intercept**:
To find the y-intercept, set \(x = 0\) in the line equation:
\[
y = -0 - 2 = -2
\]
Therefore, the y-intercept is \((0, -2)\).

4. **X-intercept**:
To find the x-intercept, set \(y = 0\) in the line equation:
\[
0 = -x - 2 \\
x = -2
\]
Therefore, the x-intercept is \((-2, 0)\), which is one of our given points.

Now let's summarize true statements about the line:

- The slope of the line is \(-1\).
- The line crosses the y-axis at \((0, -2)\).
- The line has an x-intercept at \((-2, 0)\).

From the computations and corresponding interpretations of these characteristics, any statements validating these points can be marked as true. If you have specific statements, please share them, and I can confirm which are true based on the calculations.