Question

Which inequality is represented by the graph?y > -2/3x + 1y < -2/3x + 1y < -3/2x + 1y > -3/2x + 1

Answer 1

Answer:

$y < -\frac{3}{2}x+1$

Step-by-step explanation:

Given:

From the graph shown,

The broken line means that the inequality sign will be either < or >.

The shaded region is to the left of the broken line. This means that $y < f(x)$.

Now, in order to find equation of line, we need slope and y-intercept.

From the graph, the y intercept is at $(0,1)$. So, y intercept is 1.

Also, if we consider two points $(0,1)\textrm{ and }(2,-2)$ on the line, then slope is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-2-1}{2-0}=\frac{-3}{2}=-\frac{3}{2}$

Therefore, the equation of the line is given as:

$y=mx+b\\y=-\frac{3}{2}x+1$

But as the shaded region is to the left of the line,

∴ $y$ is the correct answer.