How do you graph #6x+3y=9# by plotting points?

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Answer 1 · 2017-12-19T17:46:13

See a solution process below:

To graph a linear equation you just need to plot two points. First, solve for two points which solve the equation and plot these points:

First Point: For #x = 0#

#(6 * 0) + 3y = 9#

#0 + 3y = 9#

#3y = 9#

#(3y)/color(red)(3) = 9/color(red)(3)#

#y = 3# or #(0, 3)#

Second Point: For #y = 1#

#6x + (3 * 1) = 9#

#6x + 3 = 9#

#6x + 3 - color(red)(3) = 9 - color(red)(3)#

#6x + 0 = 6#

#6x = 6#

#(6x)/color(red)(6) = 6/color(red)(6)#

#x = 1# or #(1, 1)#

We can next plot the two points on the coordinate plane:

graph{(x^2+(y-3)^2-0.025)((x-1)^2+(y-1)^2-0.025)=0 [-10, 10, -5, 5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(6x + 3y - 9)(x^2+(y-3)^2-0.025)((x-1)^2+(y-1)^2-0.025)=0 [-10, 10, -5, 5]}