In a plane, if one line has an undefined slope and another line has a slope of zero, what can you conclude?
If one line has an undefined slope and another line has a slope of zero, it can be concluded that the two lines are perpendicular to each other.
If one line has an undefined slope and another line has a slope of zero, it means that the lines are perpendicular to each other.
A line with an undefined slope is a vertical line, meaning it goes straight up and down. This line does not have a defined slope because the change in y-coordinate is infinite while the change in x-coordinate is zero.
A line with a slope of zero is a horizontal line, meaning it goes straight left and right. This line has a slope of zero because the change in y-coordinate is zero while the change in x-coordinate is not zero.
Since vertical and horizontal lines are always perpendicular to each other, we can conclude that the two given lines are perpendicular.
To answer this question, we need to understand the properties of slopes in a coordinate plane.
First, let's clarify what it means for a line to have an undefined slope and a slope of zero.
1. Undefined slope: A line has an undefined slope when it is vertical. This happens when the line is parallel to the y-axis, and there is no change in the x-coordinate while the y-coordinate varies. In this case, the slope is said to be "undefined" because division by zero is not defined mathematically.
2. Slope of zero: A line has a slope of zero when it is horizontal. This occurs when the line is parallel to the x-axis, and there is no change in the y-coordinate while the x-coordinate varies. In this case, the slope is zero because there is no vertical change.
Now, if one line has an undefined slope and another line has a slope of zero, we can conclude that the lines are perpendicular to each other.
Perpendicular lines are lines that intersect each other at a right angle (90 degrees). The product of their slopes is -1. When one line has an undefined slope (vertical line) and another line has a slope of zero (horizontal line), the product of their slopes is 0*(-1) = 0.
Therefore, we can conclude that the two lines are perpendicular to each other when one has an undefined slope and the other has a slope of zero.