Question

How do you graph `\frac { 2} { 3} x = 6y - 8`?

Answer 1

`y=1/9x+4/3`

Explanation:

Firstly we need to rearrange the equation into standard form, which is,

`y=mx+c`

where m is the gradient and c is the y-axis intercept.

so to rearrange,

`2/3x=6y-8`

`-6y=-2/3x-8`

`6y=2/3x+8`

`y=2/(3*6)x+8/6`

`y=1/9x+4/3`

so usually when graphing i plot the y-intercept first which is at `(0,y)`

`y=1/9(0)+4/3`

`y=4/3` `=> (0,4/3)`

I then use the gradient `1/9` to determine other points.

The gradient, is defined as `"rise"/"run"`

so for our graph (`1/9`) for every 1 unit we go up we go 9 right

or, for every one unit we go down we go 9 left.

so we use this to graph subsequent points.

`(0,4/3)`

`(0+1,9+4/3) = (1,31/3)`

`(1+1,31/3+9)= (2,58/3)`

so we now graph the points we have on graphed paper.

And draw a straight line between them that continues as long as possible.

for example,

graph{1/9x+4/3 [-5, 20, -5, 5]}

Hope this helped.