Question

Which inequality is represented by the graph?

Answer 1

Answer:

Option B

Step-by-step explanation:

Notice that the region of the inequality is bounded by a line.

The first thing to do is find the equation of this line.

Note that the line intersects the x-axis at $x = 3.5$ and intercepts the y-axis at $y = -2.5$

We know that the equation of a line has the following form:

$y = mx + b$

Where m is the slope of the line and b is the intercept with the y axis.

So we already know that:

$b = -2.5 = -\frac{5}{2}$

Then we know that when $x = 3.5$ then $y = 0$

Thus:

$0 = 3.5m -2.5$

Ahroa we clear m.

$m = \frac{2.5}{3.5}\\\\m = \frac{5}{7}$

Then, the equation of the line is:

$y = \frac{5}{7}x -\frac{5}{2}$

We can also multiply by -2 both sides of the equation and we have:

$-2y = -\frac{10}{7}x +5$

Then:

$\frac{10}{7}x -2y =5$

The option that contains this equation is option B.

To verify it, enter a point within the shaded region, such as the point (0,0), in the selected inequality. If the inequality is satisfied then option B is correct

$\frac{10}{7}x -2y\leq5\\\\\frac{10}{7}(0) -2(0)\leq5\\\\0\leq5$

The inequality is satisfied because 0 is less than 5. Then the correct option is B