Question

Which linear inequality is represented by the graph?1. y>2/3x-22. y<2/3x+23. y

Answer 1

To identify the inequality of the given graph:

1. Identify the equation of the borderline in slope-intercept form (y=mx+b)

- Find the slope (m): Use two points in the line in the next formula:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ Points\colon(-3,-3)and(3,1) \\ \\ m=(1-(-3))/(3-(-3))=(1+3)/(3+3)=(4)/(6)=(2)/(3) \end{gathered}`

- Identify the y-intercept (b): the value of y where the line cross the y-axis (when x is 0)

b= -1

Equation of the border line:

`y=(2)/(3)x-1`

2, Identifify the inequality sing:

-When the inequality is < or > the borderline is a dotted line

-When the inequality is ≥ or ≤ the border line is a full line

-When the inequality is < or ≤ the shaded area is under the borderline

-When the inequality is > or ≥ the shaded are is over the borderline

In this case you have a dotted borderline and a shaded area under the borderline, then, the inequality is:

`y<(2)/(3)x-1`