Answer:
Hi can you please tell of which grade question is this ?
Yes this is the correct answer. The slope field shown is the differential equation dy/dx = x+y
All points along the line x+y = k, for some constant k, will have the same tangent slope k. For example, the line x+y = 0 will have every point with tangent slope 0 for the solution y(x). It may not be 100% clear, but this graph has horizontal tickmarks on the line x+y = 0, or the tickmarks are close to being horizontal. Using geogebra, I checked the others and they produced completely different graphs, which allowed me to rule them out.
The question is asking which of the following does not have side that are parallel. So which of them have lines that would never touch if they were never ending lines.
For each equation give X a value and solve for Y, do this at least two times for each equation.
Plot those dots on a graph to draw two lines.
The solution is where the two lines cross.
You will see the lines cross at (-1,-2)
