Aims Grade 8 Mathematics Sample Test And Think-Throughs With Answers Page 19
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36December 2009
Which statement is true?
9
All vertical lines have a slope of zero.
A
All vertical lines have a positive slope.
B
All vertical lines have a negative slope.
C
All vertical lines have an undefined slope.
D
The question is asking me to decide which statement is true. Therefore,
I must read through each statement and carefully think about what each
one means. First I will draw a vertical line so I can visualize as I think.
Choice A states…All vertical lines have a slope of zero.
This statement is saying that every line that is vertical, or straight up and down, has a slope of
zero. I remember that slope is how steep a line is counting from left to right, like if I were climbing
up or going down a hill. If a slope is zero, that means there is no change in how steep it is. If
there is no slant at all, that sounds like it would be a horizontal line.
This statement cannot be true.
Choice B states…All vertical lines have a positive slope.
When a slope is positive, that means the slope is slanting up from left to right, like if I was climbing
a hill. Looking back at my drawing of the vertical line, this line is straight
up and down. It does not have a slant. This statement cannot be true.
Choice C states…All vertical lines have a negative slope.
This is like the opposite of choice B. When a slope is negative,
that means the slope is slanting down from left to right, like if I was
going down a hill. Looking back at my drawing of the vertical line, this line
is straight up and down. It does not have a slant. This statement cannot be true.
Choice D states…All vertical lines have an undefined slope.
If a slope is undefined, that means it has a rise, how much the line goes up, but no run, how much
it moves across. Since a vertical line is only up and down, with no across, this statement sounds
true. So, my answer is choice D.
Another way to think about this problem would be to plot two points of a vertical line on a
coordinate grid. I could count the rise (y-axis units) and divide it by the run (x-axis units). I would
get a 0 for the x-axis units. When 0 is the denominator of a fraction, it is undefined.
Arizona Department of Education
19
Grade 8
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