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

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Answer 1 · 2016-10-26T06:34:51

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

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.