On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). everything below and to the right of the line is shaded.
which linear inequality is represented by the graph?
y > two-thirdsx – 2
y < two-thirdsx + 2
y > two-thirdsx + 1
y < two-thirdsx – 1

The inequality is represented by  

Use the information about the straight line and find the equation of the line.

Given coordinates and find the slope

Slope,  

Change in  

Change in  

Equation of line using    and points  and    in form of  

To find the inequality take a point in the shaded region and check it in the above equation.

For example take point  

Learn more about Inequalities.

link

y < Two-thirdsx – 1

Step-by-step explanation:

use the information about the straight line to find equation of the line.

Given coordinates (-3,-3) and (3,1) find the slope

Slope, m=change in y/change in x

Change in y= 1--3=4

Change in x=3--3=6

m=4/6=2/3

Equation of line using m=2/3  and points (3,1) and (x,y) inform of y=mx+c

To write the inequality take a point in the shaded region and test it in the above equation

For example taking point (4,1)

answer is 144

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4