Question

Which graph best represents the following inequality? y≤-5/6x+2/3

Answer 1

Answer: Second option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the following inequality:

$y\leq-\frac{5}{6}x+\frac{2}{3}$

We can identify that the line is:

$y=-\frac{5}{6}x+\frac{2}{3}$

Then:

$m=-\frac{5}{6}\\\\b=\frac{2}{3}\approx0.66$

Therefore, the slope is negative and the line intersects the y-axis at the point $(0,0.66)$

Since the symbol of the inequality is $\leq$, we can conclude that the line is solid and the shaded region is below the line. Therefore, the graph that best represents the given inequality is the second graph.