Question

Which of the following inequalities is best represented by this graph?

Answer 1

Are you given options for the answer?

Answer 2

these are the option:
x - 2y > 3
x - 2y < 3
2x – y > 3
2x – y < 3

Answer 3

@Nnesha

Answer 4

can you help me @Michele_Laino

Answer 5

From your drawing, I see thta your line passes at points A = (-1,-2) and B=(3,0), so its equation, is:
\[\begin{gathered}
x - 2y = 3 \hfill \\
{\text{or}}: \hfill \\
y = \frac{x}{2} - \frac{3}{2} \hfill \\
\end{gathered} \]

Answer 6

oops.. I see that...

Answer 7

I dont understand

Answer 8

I said that the equation of the line which divide the entire plane in two half planes has the subsequent equation:
\[y = \frac{x}{2} - \frac{3}{2}\]

Answer 9

namely the equation of the dotted line in your drawing

Answer 10

Oh ok

Answer 11

But thats not an answer..

Answer 12

now the shaded region, represented in your drawing is the region of all points whose y-coordinate is less than the y-coordinate of the points which belong to the line:
\[y = \frac{x}{2} - \frac{3}{2}\]

Answer 13

in other words, we have:
\[y < \frac{x}{2} - \frac{3}{2}\]

Answer 14

oh ok!

Answer 15

now we have to multiply both sides of that inequality by 2, what do you get?