Find an equation of the line passing through the pair of points.(−7, 1), (−7, 8)

To find the equation of the line passing through the points \((-7, 1)\) and \((-7, 8)\), we first calculate the slope. 

### Step 1: Find the slope
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

For the points \((-7, 1)\) and \((-7, 8)\):

\[
m = \frac{8 - 1}{-7 - (-7)} = \frac{7}{0}
\]

Since the denominator is 0, the slope is undefined. This means the line is vertical.

### Step 2: Find the equation
A vertical line has the equation of the form:

\[
x = c
\]

Where \(c\) is the constant \(x\)-coordinate of the points. In this case, both points have an \(x\)-coordinate of \(-7\).

Thus, the equation of the line is:

\[
x = -7
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do you find the equation of a line when the slope is defined?
2. What is the equation of a horizontal line?
3. How can you derive the equation of a line in slope-intercept form?
4. How can you calculate the distance between two points?
5. What is the midpoint formula?

**Tip:** Vertical lines always have the equation \(x = \text{constant}\), where the constant is the \(x\)-coordinate of any point on the line.

Find an equation of the line passing through the pair of points. (−7, 1), (−7, 8)

Learn how to find the equation of a vertical line passing through the points (-7, 1) and (-7, 8). This problem explains key concepts like the slope formula, how vertical lines have undefined slopes, and how to write the equation x = constant. Suitable for students in Grades 8-10.

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