Answer: No, it's not a good model
Explanation:
Let's plug in x = 8 and y = 5. This is directly from the ordered pair (8,5).
7x - 10y = 3
7*8 - 10*5 = 3
56 - 50 = 3
6 = 3
We get a false equation at the end, which means the original equation is false when (x,y) = (8,5). Therefore, the point (8,5) is not on the line 7x-10y = 3. Furthermore it means that 7x-10y = 3 is not a good model since Devon wanted the line to pass through both given points.
If you were to plug in (x,y) = (-12,-9), then you would find the same thing happens. For each ordered pair, the left side results in 6. So if Devon were to change that "3" to "6", then it would be a good model as both points would be on the line. In other words, the standard form equation Devon should use is 7x-10y = 6. When solving for y, Devon would get y = (-7/10)x - 3/5
Below is visual confirmation that 7x-10y = 3 is not a good model. Both points are not on the line. The graph was made using GeoGebra.
