The graph of a linear equation cointains the points (4,1) and (-2,-11). which pint also lies om the graph

An easy way to answer this problem is to find the mid-point between the two given points, namely  ( (4-2)/2, (1-11)/2 )=(1,-5).

Another way is to find a line through the two points, and select any point on the line.
Slope = (1-(-11))/(4-(-2))=12/6=2
Then use the point slope form to find the line:
y-1=2(x-4)  which can be simplified to
y=2x-7
Put x=0, y=-7  => (0,-7)
Put x=1, y=-5  => (1, -5)   [ as above ]
Put x=2, y=-3  => (2, -3)