Explanation:
the problem definition is wrong. there are no linear equalities here. the graphed one and all 4 answer options are linear inequalities.
anyway, if we replace the inequality signs by "=" we get the definitions of the border lines of the solution areas.
when these lines cross with the graphed line, then, of course, the lines have one point in common and the inequalities share corresponding areas.
the only case where inequalities have no shared solution areas is when the border lines are parallel, and the inequality directing are pointing in opposite directions.
lines are parallel only when they have the same slope (the factor of x).
the graphed inequality border line has the slope -5/2 (again, the factor of x).
as explained, the correct answer option must have the same slope.
the only one is the second answer option :
y < -(5/2)x - 7
as you can see, also the second criteria (opposite direction of the inequality sign) applies.
and the y-intercept is -7 and below the y-intercept of the graphed inequality (-3). so, there is no overlap of the solution areas.