Graph each of the following lines without using a table of values. a. y = 2⁄3x - 5 b. 6x - 2y + 5 = 0

(See explanation below for further details).

Step-by-step explanation:

The procedure for plotting each line consists in creating a table with at least two different points, given that Euclidean Geometry states that any line can be created with only two points,  and plotting the lines with the help of graphing tools:

(a)

(i) Table of values

       x              y

      -2         -6.333

      -1          -5.667

       0             -5

       1          -4.333  

       2         -3.667      

(ii) Plotting the line

The line is presented below in the attachment "line_1".

(b)

(i) Table of values

       x              y

      -2           -3.5

      -1            -0.5

       0            2.5

       1             5.5  

       2            8.5    

(ii) Plotting the line

The line is presented below in the attachment "line_2".

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet