Which statement is true?
A. All vertical lines have a slope of zero.
B. All vertical lines have a slope positive slope.
C. All vertical lines have a negative slope.
D. All vertical lines have a undefined slope.
WHY?
Answer = D.
m = Y/X = Y/0 = Infinite = Undefined.
The correct statement is D. All vertical lines have an undefined slope.
To understand why this is true, let's first discuss what slope represents. In geometry and algebra, slope is a measure of how steep a line is and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
Now, let's consider a vertical line. A vertical line is one that goes straight up and down, parallel to the y-axis on a coordinate plane. Since a vertical line is perfectly vertical, it does not have any horizontal change or run. This means that the denominator for the slope formula would be zero, which leads to an undefined value.
Specifically, the slope formula is (y2 - y1) / (x2 - x1). When dealing with a vertical line, any points on the line will have the same x-coordinate. So, for example, if we take two points with the same x-coordinate, say (a, b) and (a, c), we would have (c - b) / (a - a), which simplifies to (c - b) / 0. Division by zero is undefined in mathematics, resulting in an undefined slope.
Therefore, option D is correct: All vertical lines have an undefined slope due to the absence of a horizontal change or run.