A line with an undefined slope passes through the points (-2,1) and (p, q).
Which of the following points could be (p, q)?
A. (1,0)
B. (0,1)
C. (0,-2)
D. (-2,0)
Help Me, I do not know how to figure this out?????
What would make a slope undefined?
A slope is defined as the change in y over the change in x. (Or vice versa).
Hint: Anything divided by zero is undefined.
So wat do I do?
do I divide y by x?
To determine which of the given points could be (p, q), we need to find the equation of the line passing through the points (-2,1) and (p,q), and then see which of the given points satisfy this equation.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this case, we have the points (-2,1) and (p,q). Since the slope is undefined, it means that the line is vertical. In a vertical line, the x-coordinates of all the points on the line are the same.
Therefore, we know that the x-coordinate of the point (p, q) will be the same as the x-coordinate of the point (-2,1), which is -2. So, p = -2.
Now let's go through the given points and substitute p = -2 and see if the y-coordinates match with q.
A. (1,0): When p = -2, the y-coordinate should be 1 (matching with q). However, the y-coordinate is 0, so this point is not a possibility.
B. (0,1): When p = -2, the y-coordinate should be 1 (matching with q). However, the y-coordinate is also 1, so this point is a possibility.
C. (0,-2): When p = -2, the y-coordinate should be 1 (matching with q). However, the y-coordinate is -2, so this point is not a possibility.
D. (-2,0): When p = -2, the y-coordinate should be 1 (matching with q). However, the y-coordinate is 0, so this point is not a possibility.
The only point that satisfies the equation of the line passing through (-2,1) and (p,q) is (0,1). So, the answer is B. (0,1).
To determine which of the given points could be (p, q), we need to consider the concept of undefined slope.
The slope of a line is defined as the change in y-coordinates divided by the change in x-coordinates between two points on the line. However, if the line has an undefined slope, it means that the change in x-coordinates is zero or there is no change. In other words, the line is a vertical line.
Now let's examine the given points: (-2,1) and (p, q).
If a line with an undefined slope passes through the points (-2,1) and (p, q), it means that the x-coordinate must be the same for both points. In other words, p = -2.
Now, let's go through each of the given answer choices and substitute p = -2 to check if the y-coordinate matches q:
A. (1,0): When p = -2, the point becomes (-2,0), which does not match the y-coordinate q = 1. Therefore, this point cannot be (p, q).
B. (0,1): When p = -2, the point becomes (-2,1), which matches the y-coordinate q = 1. Therefore, this point could be (p, q).
C. (0,-2): When p = -2, the point becomes (-2,-2), which does not match the y-coordinate q = 1. Therefore, this point cannot be (p, q).
D. (-2,0): When p = -2, the point becomes (-2,0), which does not match the y-coordinate q = 1. Therefore, this point cannot be (p, q).
Based on this analysis, the point (0,1) (option B) could be (p, q) for a line with an undefined slope passing through the points (-2,1) and (p, q).