Question

This graph shows the solution to which inequality?

Answer 1

`m=(y2-y1)/(x2-x1) \\ \\ m=(2-(-6))/(3-(-3)) \\ \\ m=(8)/(6) \\ \\ m=(4)/(3)`

The y-intercept of the graph is -2

The graph is shaded upwards, so we will be using the greater than symbol, but since the line is dotted we will not be using any of the "equal to" symbols.

Hence, the solution of the graph is
`y>m=(4)/(3) x-2`

Answer 2

Option: C is the correct answer.

C.
`y>(4)/(3)x-2`

Explanation:

By looking at the graph we observe that the line is dotted this means that the inequality will be strict.

Also, this line passes through the point (-3,-6) and (3,2).

Hence, the equation of line is calculated by using a two point form i.e. a line passing through two points (a,b) and(c,d) is calculated with the help of formula as:

`y-b=(d-b)/(c-a)* (x-a)`

Here (a,b)=(-3,-6) and (c,d)=(3,2)

i.e.

`y-(-6)=(2-(-6))/(3-(-3))* (x-(-3)}\\\\i.e.\\\\y+6=(2+6)/(3+3)* (x+3)\\\\i.e.\\\\y+6=(8)/(6)* (x+3)\\\\i.e.\\\\y+6=(4)/(3)* (x+3)\\\\i.e.\\\\y+6=(4)/(3)x+4\\\\i.e.\\\\y=(4)/(3)x-2`

Also, the shaded region is towards the origin.

Hence, the inequality is:

`y>(4)/(3)x-2`