How do you graph #3x + 5y = 6# by plotting points?

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Answer 1 · 2018-04-07T15:36:02

See a solution process below:

First, solve for two points which solve the equation and plot these points:

First Point: For #y = 0#

#3x + (5 * 0) = 6#

#3x + 0 = 6#

#3x = 6#

#(3x)/color(red)(3) = 6/color(red)(3)#

#x = 2# or #(2, 0)#

Second Point: For #y = 3#

#3x + (5 * 3) = 6#

#3x + 15 = 6#

#3x + 15 - color(red)(15) = 6 - color(red)(15)#

#3x + 0 = -9#

#3x = -9#

#(3x)/color(red)(3) = -9/color(red)(3)#

#x = -3# or #(-3, 3)#

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

graph{((x-2)^2+y^2-0.035)((x+3)^2+(y-3)^2-0.035)=0 [-10, 10, -5, 5]}

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

graph{(3x+5y-6)((x-2)^2+y^2-0.035)((x+3)^2+(y-3)^2-0.035)=0 [-10, 10, -5, 5]}