Find the slope of the line that passes through and . Write your answer in simplest form.
Select “Undefined” if applicable.

Question

Find the slope of the line that passes through $$ (-4,5) $$ and $$ (-4,-2) $$. Write your answer in simplest form. Select "Undefined" if applicable.

UpStudy AI · Accepted Answer

To find the slope of the line passing through the points $$(-4, 5)$$ and $$(-4, -2)$$, we can use the slope formula:

$$
\text{Slope} (m) = \frac{y_2 - y_1}{x_2 - x_1}
$$

Let's plug in the given points:

$$
x_1 = -4,\ y_1 = 5 \
x_2 = -4,\ y_2 = -2
$$

Now, calculate the differences:

$$
y_2 - y_1 = -2 - 5 = -7 \
x_2 - x_1 = -4 - (-4) = 0
$$

So, the slope formula becomes:

$$
m = \frac{-7}{0}
$$

Division by zero is undefined in mathematics. This situation indicates that the line is **vertical**, and vertical lines have an **undefined slope**.

**Answer:** Undefined
The slope is undefined.

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