What is an equation of the line that passes through the points left parenthesis, minus, 4, comma, 5, right parenthesis(−4,5) and left parenthesis, minus, 4, comma, minus, 2, right parenthesis(−4,−2)?

To find the equation of the line passing through the points \((-4, 5)\) and \((-4, -2)\), we need to consider the slope and type of the line.

### Step 1: Determine the slope

The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substituting the coordinates of the points:

\[
m = \frac{-2 - 5}{-4 - (-4)} = \frac{-7}{0}
\]

Since the denominator is zero, the slope is undefined, which means the line is vertical.

### Step 2: Write the equation

For a vertical line, the equation is always of the form \(x = c\), where \(c\) is the constant x-coordinate of the points through which the line passes. Since both points have the same x-coordinate, \(-4\), the equation of the line is:

\[
x = -4
\]

Thus, the equation of the line is \(x = -4\).

Would you like any further explanation or details?

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Here are some related questions you might find useful:

1. What is the equation of a line with a positive slope?
2. How do you find the equation of a horizontal line?
3. What happens when the slope of a line is zero?
4. Can two points define a unique vertical line? Why?
5. How do parallel and perpendicular slopes relate?

**Tip:** A vertical line has an undefined slope because the change in \(x\) is zero, making the denominator in the slope formula zero.

What is an equation of the line that passes through the points (−4,5) and (−4,−2)?

This page provides a detailed solution to finding the equation of the vertical line passing through the points (-4, 5) and (-4, -2). Learn how to determine the undefined slope and the equation of a vertical line, suitable for Grades 8-10.

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