Ellen thinks that if a line has no slope, then it never touches the y-axis. Which line proves that her statement is incorrect?
x = 0
y = 0
x = 1
y = 1
It x=0
So it's y or x = 0?
y = 0
These represent the x-axis whose slope is 0 and intersects the y-axis at the beginning.
x=0
This is a line which is vertical, and is the y-axis.
It has a slope which is undefined.
So pick which answer reflects your idea of "no slope."
If there is no difference in the x-axis, it becomes undefined, or vertical. But, if there is a difference in the y-axis, or if it is zero, it becomes horizontal. I put it down to two choices: x = 0 and y = 1. The y-axis would have been touched if it had been brought to 1. x=0 doesn't do anything about the y-axis, but it makes it vertical. And, what it looks like to other people, choose x = 0.
It is x = 0. I did the test
To determine which line proves Ellen's statement incorrect, we need to understand the equation of a line and how it relates to the slope and the y-axis.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
Let's analyze each of the given lines:
1. x = 0:
This equation represents a vertical line parallel to the y-axis, where the x-coordinate is always 0. The slope of a vertical line is undefined. However, this line does intersect the y-axis at the point (0, b), where b can be any real number. Therefore, this line does not support Ellen's statement, as it does touch the y-axis.
2. y = 0:
This equation represents a horizontal line parallel to the x-axis, where the y-coordinate is always 0. The slope of a horizontal line is 0. Since this line lies on the x-axis itself, it intersects the y-axis at the origin (0, 0). So, this line does touch the y-axis. Therefore, this line does not prove Ellen's statement wrong.
3. x = 1:
This equation represents a vertical line parallel to the y-axis, where the x-coordinate is always 1. Similarly to the first example, the slope of a vertical line is undefined. This line intersects the y-axis at the point (1, b), where b can be any real number. Therefore, this line does not support Ellen's statement, as it does touch the y-axis.
4. y = 1:
This equation represents a horizontal line parallel to the x-axis, where the y-coordinate is always 1. The slope of a horizontal line is 0. Since this line lies above the x-axis at the point (x, 1), it intersects the y-axis at the point (0, 1). Therefore, this line touches the y-axis.
To prove Ellen's statement incorrect, we can conclude that the line expressed by the equation x = 0 is the line that contradicts her claim.