Step-by-step explanation:
the second line has to be parallel (but not identical), so that the 2 lines do not cross each other, do not have any point in common.
that means it must have the same slope but a different y-intercept.
the line in the graph goes through the origin (0, 0), which makes the y-intercept = 0 (the y value when x = 0).
and we see that the points with integer coordinates seem to be e.g. (3, -2).
so, for the slope (y difference / x difference between 2 points) we use this point and the origin.
x changes by +3 (from 0 to 3).
y changes by -2 (from 0 to -2).
so, the slope is -2/3. and it is always the factor of x.
let's look at the answer options :
2x + 3y = 0
3y = -2x
y = (-2/3)x
this is the identical line, so it is wrong !
2x + 3y = 6
3y = -2x + 6
y = (-2/3)x + 2
the same slope and different y-intercept.
this is the correct solution !
2x - 3y = 9
-3y = -2x + 9
y = (2/3)x - 3
wrong slope. so it is wrong !
y = 3x + 2
wrong slope. so it is wrong !
