Question

Which graph correctly represents (5/2)x - y < 3?

Answer 1

(5/2)x - y < 3

-y < -(5/2)x + 3

y > (5/2)x - 3

The answer is B

Answer 2

You can rewrite the inequality as

$y > \cfrac{5}{2}\ x - 3$

Note that

$y = f(x) = \cfrac{5}{2}\ x - 3$

is the equation of the line drawn in the pictures. This means that, for every point on the line, the y coordinate is exactly image of the x coordinate, i.e. $f(x)$

The inequality is satisfied by all points whose y coordinate exceeds the image of the x coordinate. Since the y axis is positively oriented upwards, a greater value for the y coordinate means that the point has to be higher than the line.

Also, since the equality inlves a $>$ and not a $\geq$ sign, the line itself is excluded.

So, the correct graph is the second one.