Question

which of the geoboards shown below models a slope of - 2? select the correct answer below:

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{\text{rise}}{\text{run}}$. A slope of $- 2$ means $\frac{\text{rise}}{\text{run}}=-2=\frac{-2}{1}$ or $\frac{2}{-1}$, which implies for every 1 - unit increase in the $x$ - direction (run), the $y$ - value decreases by 2 units (negative rise), or for every 1 - unit decrease in the $x$ - direction, the $y$ - value increases by 2 units.

Step2: Analyze geoboard models

On a geoboard, count the number of units in the horizontal (run) and vertical (rise) directions between the two endpoints of the rubber - band representing the line. Check each geoboard to see if the ratio of the vertical change to the horizontal change is $-2$.

Answer:

Since no specific details about the geoboard models are given in text (only a picture reference), in a general sense, look for a geoboard where for a right - ward movement of 1 peg, the rubber - band goes down 2 pegs (or for a left - ward movement of 1 peg, it goes up 2 pegs). Without seeing the actual visual details of each option clearly, we can't definitively point out which one it is from the text description alone. But the method to find the answer is to use the slope formula $m = \frac{\text{rise}}{\text{run}}=-2$ and count the pegs on the geoboard for rise and run.