What of the following statements describes a zero slope? Check all that apply.
The line goes up when moving right to left.
The line goes down when moving right to left.
The line is horizontal.
The line is vertical.
The run is zero.
The rise is zero.
The line is horizontal.
The rise is zero.
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1+1
1+1 = 2
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A 2-column table with 5 rows. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4. Column 2 is labeled y with entries 19, 16, 13, 10, 7.
Use the values in the table to determine the slope.
m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction
none
Three-halves
0
Negative three-halves
m = StartFraction y2 - y1 Over x2 - x1 EndFraction
Using the given values in the table, let's choose any two points:
(x1, y1) = (-4, 19)
(x2, y2) = (4, 7)
Substituting these values in the slope formula, we get:
m = (7 - 19) / (4 - (-4))
m = -12/8
m = -3/2
Therefore, the slope of the line passing through the five given points is negative three-halves.
A zero slope means that the line is horizontal. When calculating the slope of a line, you compare the change in the y-coordinates (rise) to the change in the x-coordinates (run). A zero slope indicates that there is no change in the y-coordinates, meaning the line neither goes up nor down. Therefore, the following statement applies:
- The line is horizontal.
To check if the line has a zero slope, you can also examine the values of the rise and run.
- The rise refers to the change in the y-coordinates. If the rise is zero, it means there is no vertical change in the line. Therefore, the following statement also applies:
- The rise is zero.
However, the other statements describing a zero slope do not apply:
- The line goes up when moving right to left: This describes a positive slope.
- The line goes down when moving right to left: This describes a negative slope.
- The line is vertical: This describes an undefined slope (division by zero).
- The run is zero: A zero run would not be valid as it would result in division by zero when calculating the slope.