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

Question

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

Julia Adams · Accepted Answer

See the explanation below.

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]}

Avery Alexander · Answer

undefined To graph the equation $ y - 2 = \frac{2}{3}(x - 4) $, you can follow these steps:

1. Start with the equation in slope-intercept form, $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.
2. Rewrite the given equation in slope-intercept form by isolating $ y $.
3. Once you have the equation in slope-intercept form, identify the slope and y-intercept.
4. Plot the y-intercept on the y-axis.
5. Use the slope to find another point on the line, typically by moving vertically and horizontally from the y-intercept according to the slope.
6. Draw a straight line through the two points to represent the graph of the equation.