Question

6. Which inequality has the solution set shown in the graph below? cont OTTO -7 -6 -5 -4 -3-2-1-1 1 2 3 4 5 6 7 T

Answer 1

First we need write the equation of the line

we start from the general equation

`y=mx+b`

we need find m(slope) and b(cut point)

for the slope

we choose 2 points and find

(0,5)and(1,3)

`\begin{gathered} m=(y2-y1)/(x2-x1) \\ \\ m=(3-5)/(1-0) \\ m=-(2)/(1) \\ m=-2 \end{gathered}`

the slope is -2

we can replace on the general equation with a point(0,5) and solve b

for b

`\begin{gathered} y=(-2)x+b \\ 5=(-2)(0)+b \\ 5=0+b \\ b=5 \end{gathered}`

replacing m and b, the final equation is

`y=-2x+5`

now, our inequality tells us that it takes into account the values ​​below the line without taking the line (because it is dotted)

so we change = for <

the inequality is

`y<-2x+5`