Let's solve each problem step-by-step to find the slope of the lines passing through the given points.
### Slope of the line passing through (-5, 9) and (-5, -7)
1. Identify the coordinates:
- Point 1, [tex]\( (x_1, y_1) = (-5, 9) \)[/tex]
- Point 2, [tex]\( (x_2, y_2) = (-5, -7) \)[/tex]
2. Recall the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Substitute the coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{-7 - 9}{-5 - (-5)} = \frac{-16}{0}
\][/tex]
4. Interpret the result:
- Division by zero is not defined in mathematics. Therefore, if the x-coordinates of both points are equal, the line is vertical and the slope is undefined.
Conclusion: The slope of the line passing through the points (-5, 9) and (-5, -7) is undefined.
### Slope of the line passing through (-2, -3) and (5, -3)
1. Identify the coordinates:
- Point 1, [tex]\( (x_1, y_1) = (-2, -3) \)[/tex]
- Point 2, [tex]\( (x_2, y_2) = (5, -3) \)[/tex]
2. Recall the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Substitute the coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{-3 - (-3)}{5 - (-2)} = \frac{0}{7} = 0
\][/tex]
4. Interpret the result:
- Since the numerator is zero, the slope is 0. When the y-coordinates of both points are equal, the line is horizontal.
Conclusion: The slope of the line passing through the points (-2, -3) and (5, -3) is [tex]\( 0 \)[/tex].
### Final Answers
- Slope of the line passing through (-5, 9) and (-5, -7) is undefined.
- Slope of the line passing through (-2, -3) and (5, -3) is [tex]\( 0 \)[/tex].
