Answer :
To determine the slope of the line that passes through the points [tex]\((6, 10)\)[/tex] and [tex]\((6, -2)\)[/tex], follow these steps:
1. Identify the coordinates of the points:
- Point 1: [tex]\((x_1, y_1) = (6, 10)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (6, -2)\)[/tex]
2. Calculate the change in the y-coordinates ([tex]\(\Delta y\)[/tex]):
[tex]\[ \Delta y = y_2 - y_1 = -2 - 10 = -12 \][/tex]
3. Calculate the change in the x-coordinates ([tex]\(\Delta x\)[/tex]):
[tex]\[ \Delta x = x_2 - x_1 = 6 - 6 = 0 \][/tex]
4. Determine the slope using the formula:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} \][/tex]
Given that [tex]\(\Delta x = 0\)[/tex], this means the denominator is zero. A fraction with a zero denominator is undefined.
Therefore, the slope of the line passing through the points [tex]\((6, 10)\)[/tex] and [tex]\((6, -2)\)[/tex] is undefined, as the line is vertical.
1. Identify the coordinates of the points:
- Point 1: [tex]\((x_1, y_1) = (6, 10)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (6, -2)\)[/tex]
2. Calculate the change in the y-coordinates ([tex]\(\Delta y\)[/tex]):
[tex]\[ \Delta y = y_2 - y_1 = -2 - 10 = -12 \][/tex]
3. Calculate the change in the x-coordinates ([tex]\(\Delta x\)[/tex]):
[tex]\[ \Delta x = x_2 - x_1 = 6 - 6 = 0 \][/tex]
4. Determine the slope using the formula:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} \][/tex]
Given that [tex]\(\Delta x = 0\)[/tex], this means the denominator is zero. A fraction with a zero denominator is undefined.
Therefore, the slope of the line passing through the points [tex]\((6, 10)\)[/tex] and [tex]\((6, -2)\)[/tex] is undefined, as the line is vertical.
