https://file.aiquickdraw.com/mathbot/file/1725862363411rwxle5xr.jpg

To find the **y-intercept** of the line passing through the points \((-2, -2)\) and \((2, -4)\), we can follow these steps:

### Step 1: Find the slope (m)
The slope formula is:

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

Using the points \((-2, -2)\) and \((2, -4)\):

\[
m = \frac{-4 - (-2)}{2 - (-2)} = \frac{-4 + 2}{2 + 2} = \frac{-2}{4} = -\frac{1}{2}
\]

### Step 2: Use the point-slope form of a line equation
The point-slope form is:

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

Let's use the point \((-2, -2)\):

\[
y - (-2) = -\frac{1}{2}(x - (-2))
\]

Simplifying:

\[
y + 2 = -\frac{1}{2}(x + 2)
\]
\[
y + 2 = -\frac{1}{2}x - 1
\]
\[
y = -\frac{1}{2}x - 1 - 2
\]
\[
y = -\frac{1}{2}x - 3
\]

### Step 3: Find the y-intercept
The y-intercept occurs when \(x = 0\). Substituting \(x = 0\) into the equation \(y = -\frac{1}{2}x - 3\):

\[
y = -\frac{1}{2}(0) - 3 = -3
\]

Thus, the **y-intercept** is \((0, -3)\).

### Answer:
The correct choice is **A. (0, -3)**.

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. How do you calculate the slope between two points on a line?
2. What is the point-slope form of a line and how is it useful?
3. How does the y-intercept relate to the equation of a line?
4. How would the slope change if the two points were reversed?
5. Can the y-intercept ever be the same as one of the given points?

**Tip**: The y-intercept is always found by setting \(x = 0\) in the equation of a line.

Find the y-intercept of the line which passes through (-2, -2) and (2, -4).

Learn how to find the y-intercept of a line passing through points (-2, -2) and (2, -4) with a detailed step-by-step solution. This problem covers algebraic concepts such as the slope formula, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation