How do you graph #y-2=2/3(x-4)#?

1 Answer
Meave60
Jun 28, 2017

See the explanation below.

Explanation:

Graph:

#y-2=2/3(x-4)#

The easiest way to find points on the line is to convert the given equation in point slope form to slope intercept form: #y=mx+b#, where #m# is the slope, and #b# is the y-intercept. In order to do this, solve the point slope equation for #y#.

#y-2=2/3(x-4)#

Add #2# to both sides.

#y=2/3(x-4)+2#

Simplify #2/3(x-4)# to #(2(x-4))/3#.

#y=(2(x-4))/3+2#

Expand.

#y=(2x)/3-8/3+2#

Simplify.

#y=2/3x-8/3+2#

Multiply #2# by #3/3# to get the same denominator as #-8/3#.

#y=2/3x-8/3+2xx3/3#

Simplify.

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

#y=2/3x-2/3#

Determine two or three points on the line by choosing values for #x# and solving for #y#.

#"Points"#

#x=-2,##y=-2#

#x=0,##y=-2/3#

#x=1,##y=0#

Plot the points and draw a straight line through them.

graph{y=2/3(x-4)+2 [-12.66, 12.65, -6.33, 6.33]}

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