Question

What is the slope of the line that passes through the points left parenthesis, minus, 6, comma, 1, right parenthesis(−6,1) and left parenthesis, minus, 6, comma, minus, 4, right parenthesis(−6,−4)? Write your answer in simplest form.
dont make me fail again

Answer 1

To find the slope of a line that passes through two points, we can use the formula for slope \( m \):

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

In this case, the two points are \((-6, 1)\) and \((-6, -4)\). We can let:

- \((x_1, y_1) = (-6, 1)\)
- \((x_2, y_2) = (-6, -4)\)

Now, substituting the values into the slope formula:

\[
m = \frac{-4 - 1}{-6 - (-6)}
\]

Calculating the numerator:

\[
-4 - 1 = -5
\]

Calculating the denominator:

\[
-6 - (-6) = -6 + 6 = 0
\]

So we have:

\[
m = \frac{-5}{0}
\]

Since the denominator is zero, the slope is undefined. This indicates that the line is vertical.

In summary, the slope of the line that passes through the points \((-6, 1)\) and \((-6, -4)\) is **undefined**.