Which of the following is TRUE about the line through the points (–1, 4) and (–1, 2)?
Please EXPLAIN/SHOW WORK.
A. The slope is undefined
B. The slope is negative
C. The slope is 0
D. The slope is positive
A. The slope is undefined.
B. The slope is negative.
C. The slope is 0.
D. The slope is positive.
The slope m between two points P1(x1,y1) and P2(x2,y2) can be calculated using
m=(y2-y1)/(x2-x1) where x2≠x1
if x2=x1, and y2≠y1, it means that the line is vertical (slope is infinite or undefined)
if x2=x1 and y2=y1, the two points are coincident and the line is indefinite.
In all other cases, the slope m can be obtained by the formula above.
For the case in question,
P1(–1, 4) and P2(–1, 2)
so x2=x1=-1, and y2≠y1
Therefore the line is vertical.
Post again if you need more explanations to choose the answer.
If the line is vertical there is no slope making it undefined correct?
correct!
Sorry, it should read:
If the line is vertical the slope is infinite making it undefined.
To determine the slope of a line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (–1, 4) and (–1, 2), we can assign the coordinates (x1, y1) = (–1, 4) and (x2, y2) = (–1, 2).
Plugging these values into the formula, we get:
m = (2 - 4) / (–1 - (–1))
m = (2 - 4) / (–1 + 1)
m = –2 / 0
We can see that the denominator is 0, which means the equation is undefined. Therefore, the correct answer is A. The slope is undefined.