Graph the inequality on a coordinate plane.
-y < 3x - 5
Question 769288
How do I Graph -y < 3x - 5
We draw the boundary line which has the equation that is
like the inequality except that it has an equal sign instead
of a "<".
Boundary line's equation is -y = 3x - 5. Let's multiply that
through by -1.
y = -3x + 5
Letting x = 0, we get y = -3(0) + 5 = 5, so (0,5) is a point on the line.
Letting x - 1, we get y = -3(1) + 5 = 2, so (1,2) is a point on the line.
We plot those and draw a dotted line through them, dotted because
the solution set does not include its boundary line, since the
inequality is <, and not <.
Then we pick a test point not on the line. We can pick (0,0) since
it is not on the line. We test to see if (0,0) is a solution or not.
We substitute it in the original inequality:
-y < 3x - 5
-0 < 3(0) - 5
0 < -5
That is false, so all the solutions are on the OPPOSITE side of the
boundary line that the origin is on, so we shade the side of the line
which the origin is not on:
Edwin
