Question

Write an inequality to represent the graph.

Answer 1

Answer:

y is greater or equal to than two thirds times x minus 7

$y\geq \frac{2}{3}x-7$

Step-by-step explanation:

The first choice is the right answer.

We find the right answer by calculating the slop in first place, and then find the equation of the line. At last, we will find what inequality sign must be included.

So, according to slope's definition, we have:

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}=\frac{-5-(-7)}{3-0}=\frac{2}{3}$

Now, we know that one of the point that the solid line is intersecting is $(0;-7)$, with that detail, we know that y-axis intersection is $y=-7$, which we are gonna call $b=-7$

Then, we apply the explicit form of a line equation: $y=mx+b$

Replacing all values we have:

$y=\frac{2}{3}x-7$

Now, the problem says that the shading is above the line, when this happens, the correct inequality sign is $\geq$.

Therefore, the inequality that represents the given line is:

$y\geq \frac{2}{3}x-7$

Which is the first option.