Question

4. Which inequality is represented by the graph?8642S-6428X4-6laO4x - 2y > 12O4x - 2y < 12O4x + 2y > 12O4x + 2y < 12

Answer 1

Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.

First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:

We can easily find the points (0, -6) and (2, -2).

With this, we can find the equation of the line using the point-slope formula:

`y-y_0=m\cdot(x-x_0)`

Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:

`m=(y_1-y_0)/(x_1-x_0)`

Plugging the coordinates of the points, we get:

`m=(-2-(-6))/(2-0)=(-2+6)/(2)=(4)/(2)=2`

Such that:

`\begin{gathered} y-(-6)=2\cdot(x-0) \\ y+6=2x \end{gathered}`

Rearranging it in the ax + by = c form,

`2x-y=6`

Multiply both sides of the equation by a factor of 2

`4x-2y=12`

Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:

`4x-2y>12`

All the point (x, y) satisfying this inequality are contained in the shaded region.