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.

Question

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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.