Question

introduction to slope - item 32608
what is a simple way to tell that 1\frac{1}{2} is not the slope of this graph?
graph of a line with points a(0,2.5) and b(0.833, 0)
options:
the y-intercept is 2\frac{1}{2}, not 1\frac{1}{2}.
a slope cannot be a mixed number.
the line slants downward, so the slope is negative.
the change in x from a to b is negative.

Explanation:

To determine why \(1\frac{1}{2}\) is not the slope, we analyze the graph's direction. The line slants downward from left to right, meaning the slope (rise over run) should be negative. \(1\frac{1}{2}\) is positive, so the option "The line slants downward, so the slope is negative" correctly identifies this. Other options: y - intercept info is irrelevant to slope sign, slope being a mixed number isn't the key here, and change in x sign doesn't directly rule out \(1\frac{1}{2}\) (as slope sign depends on rise/run sign).

Answer:

The option: "The line slants downward, so the slope is negative" (the one with this text, likely the bottom - middle option based on layout).