What is an equation of the line that passes through the points (2, -8) and (-2, 0)?

To find the equation of the line that passes through the points \((2, -8)\) and \((-2, 0)\), we follow these steps:

### Step 1: Find the slope of the line
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Substitute the points \((2, -8)\) and \((-2, 0)\):

\[
m = \frac{0 - (-8)}{-2 - 2} = \frac{0 + 8}{-4} = \frac{8}{-4} = -2
\]

So, the slope of the line is \(m = -2\).

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

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

We can use one of the points, say \((2, -8)\), and the slope \(m = -2\):

\[
y - (-8) = -2(x - 2)
\]

Simplify the equation:

\[
y + 8 = -2(x - 2)
\]
\[
y + 8 = -2x + 4
\]
\[
y = -2x + 4 - 8
\]
\[
y = -2x - 4
\]

### Final equation
The equation of the line is:

\[
y = -2x - 4
\]

Let me know if you want further details or have any questions! Here are some related questions you can explore:

1. What is the y-intercept of the line \(y = -2x - 4\)?
2. How do you convert the slope-intercept form to standard form?
3. What is the distance between the two points \((2, -8)\) and \((-2, 0)\)?
4. What is the equation of a line parallel to \(y = -2x - 4\) passing through \((1, 3)\)?
5. What is the equation of a line perpendicular to \(y = -2x - 4\)?

**Tip**: When finding the slope between two points, remember to subtract the coordinates in the correct order to avoid sign errors.

Discover how to find the equation of a line passing through the points (2, -8) and (-2, 0) using the slope formula and point-slope form. This problem covers key algebraic concepts like slope and linear equations, suitable for 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