Question

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

Answer 1

(See explanation below for further details).

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)
`y = (2)/(3)\cdot x - 5`

(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)
`6\cdot x - 2\cdot y + 5 = 0`

`2\cdot y = 6\cdot x +5`

`y = 3\cdot x +(5)/(2)`

(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".