To determine the slope of the line that passes through the points (-5, 8) and (-5, 4), follow these steps:
### 1. Identify the Coordinates
First, identify the coordinates of the two points through which the line passes:
- Point 1: [tex]\((-5, 8)\)[/tex]
- Point 2: [tex]\((-5, 4)\)[/tex]
### 2. Calculate the Difference in Y-Coordinates
Next, compute the difference between the y-coordinates of the two points:
[tex]\[
\Delta y = y_2 - y_1 = 4 - 8 = -4
\][/tex]
### 3. Calculate the Difference in X-Coordinates
Then, compute the difference between the x-coordinates of the two points:
[tex]\[
\Delta x = x_2 - x_1 = -5 - (-5) = -5 + 5 = 0
\][/tex]
### 4. Determine the Slope
The formula for the slope ([tex]\(m\)[/tex]) of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the calculated differences:
[tex]\[
m = \frac{-4}{0}
\][/tex]
### 5. Identify the Nature of the Slope
When the difference in x-coordinates ([tex]\(\Delta x\)[/tex]) is 0, the divisor of the slope formula becomes zero. Dividing by zero is undefined in mathematics.
### Conclusion
Since [tex]\(\Delta x = 0\)[/tex], the slope of the line passing through the points (-5, 8) and (-5, 4) is undefined. This implies that the line is vertical.
