Question

What is the slope of the line that passes through the points left bracket, 0, comma, minus, 8, right bracket(0,−8) and left bracket, 0, comma, minus, 10, right bracket(0,−10)? Write your answer in simplest form.

Answer 1

The slope of a line passing through the points (0, -8) and (0, -10) is undefined because it represents a vertical line.

Step-by-step explanation:

The slope of a line measures its steepness, usually denoted as rise over run. To calculate the slope of a line passing through two points, (x1, y1) and (x2, y2), we use the formula:

slope (m) = (y2 - y1) / (x2 - x1)

In the question, we have two points: (0, -8) and (0, -10). Let's substitute these values into our formula:

slope (m) = (-10 - (-8)) / (0 - 0)

After simplifying the subtraction in the numerator, we get:

slope (m) = (-10 + 8) / 0

So, slope (m) = -2 / 0

Here, we have a division by zero, which is undefined. However, looking at the coordinates of the points, we can notice that they share the same x-value but have different y-values, indicating this is a vertical line. The slope of a vertical line is undefined. Hence, the slope of the line that passes through the points (0, -8) and (0, -10) is undefined.