Final answer:
Options A (Δx/Δy) and D ('run/rise') are incorrect expressions for slope. The correct formula for slope is the change in y-value over the change in x-value, or Δy/Δx, which matches option B and is also reflected correctly in option C (y2−y1/x2−x1).
Step-by-step explanation:
To address the student's question, which of the following are incorrect expressions for slope, we need to consider the definition of the slope of a line in mathematics. Slope is generally described as the change in the y-value (the rise) divided by the change in the x-value (the run) of two points on a straight line. The expressions for slope are usually given in the form of rises over run or Δy/Δx where Δ denotes a change in the variable.
Let's evaluate each expression provided:
- A. Δx/Δy is incorrect because it represents the inverse of the slope, that is, run divided by rise instead of rise over run.
- B. 'Change in the dependent variable relative to change in the independent variable' is correct as it properly describes the concept of slope.
- C. y₂−y₁/x₂−x₁ is a correct representation of slope as well because it shows the difference in y-values (rise) over the difference in x-values (run).
- D. 'run/rise' is incorrect because it should be 'rise/run' by the slope definition.
Therefore, options A and D are incorrect expressions for slope. Remember, in mathematical equations like y = mx + b, 'm' represents the slope, which is the rise divided by the run, and 'b' is the y-intercept.