To determine which expressions for slope are incorrect, let's carefully analyze each option given:
A. Change in the dependent variable relative to change in the independent variable:
This is a correct description of the slope. The slope of a line in a coordinate plane is defined as the rate of change of the dependent variable (usually [tex]\( y \)[/tex]) with respect to the independent variable (usually [tex]\( x \)[/tex]).
B. run:
This is incorrect. 'Run' specifically refers to the horizontal change (change in [tex]\( x \)[/tex]-value) between two points on a graph. Slope requires both the rise (change in [tex]\( y \)[/tex]-value) and the run (change in [tex]\( x \)[/tex]-value), not just the run alone.
C. [tex]\(\frac{\Delta y}{\Delta x}\)[/tex]:
This is correct. The slope [tex]\( m \)[/tex] is mathematically expressed as [tex]\(\frac{\Delta y}{\Delta x}\)[/tex], where [tex]\(\Delta y\)[/tex] is the change in the [tex]\( y \)[/tex]-values and [tex]\(\Delta x\)[/tex] is the change in the [tex]\( x \)[/tex]-values.
D. [tex]\(\frac{x_2 - x_1}{y_2 - y_1}\)[/tex]:
This is incorrect. The formula given here seems to be a ratio, however, it is inverted. The correct slope formula should be [tex]\(\frac{y_2 - y_1}{x_2 - x_1}\)[/tex]. This version would not yield the correct value for slope.
From our analysis, the incorrect expressions for slope are:
- B (run)
- D ([tex]\(\frac{x_2 - x_1}{y_2 - y_1}\)[/tex])
Thus, the answer is:
[2, 4]
