100 Points! Which inequality is represented by the graph? y<5/3x−3

y>5/3x−3

y<3/5x−3

y≤5/3x−3

The linear equation with slope m and intercept c is given as follows.

The formula for slope of line with points  and  can be expressed as,

Given:

The inequalities are as follows.

a.  

b.  

c.  

d.

Step-by-step explanation:

Step 1: Find equations of the lines

Red, solid line:

Find slope: 1square in y / 3 squares in x => slope = 1/3

y-intercept : (0,3)

Equation of the line: one of the following:

y=x/3+3   (1a)

3y=x+9    (1b)

x-3y+9=0 (1c)

Black, dotted line:

Slope = 3 squares in y / 1 square in x => slope = 3

y-intercept (0,-2)

Equation of the line: one of the following:

y=3x-2(2a)

3x-y=2(2b)

2. Find location of region, i.e. greater or less than

Red region:

The region is above the solid line, i.e. we look for y>=

From equation (1a), we change the equality to >=, or

y >= x/3+3   [>= because line is solid]

Black region:

The region is to the right of the dotted line, we look for x > ...

From equation (2b),, we change equality to >, or

3x-y > 2   [ > because line is dotted ]

Note: All the given answers have common typos, namely

the first inequality should read y > x/3+3   or y>=x/3+3

the second inequality should read 3x-y > 2 or 3x-y >=2

The way question is presented, all the answer choices are the same (and incorrect).

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2