How do you graph #9x + 2y = -7# by plotting points?

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Answer 1 · 2018-06-17T12:04:25

See a solution process below:

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

First Point: For #x = 1#

#(9 * 1) + 2y = -7#

#9 + 2y = -7#

#9 - color(red)(9) + 2y = -7 - color(red)(9)#

#0 + 2y = -16#

#2y = -16#

#(2y)/color(red)(2) = -16/color(red)(2)#

#y = -8# or #(1, -8)#

Second Point: For #x = -1#

#(9 * -1) + 2y = -7#

#-9 + 2y = -7#

#-9 + color(red)(9) + 2y = -7 + color(red)(9)#

#0 + 2y = 2#

#2y = 2#

#(2y)/color(red)(2) = 2/color(red)(2)#

#y = 1# or #(-1, 1)#

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

graph{((x-1)^2+(y+8)^2-0.1)((x+1)^2+(y-1)^2-0.1)=0 [-20, 20, -10, 10]}

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

graph{(9x+2y+7)((x-1)^2+(y+8)^2-0.1)((x+1)^2+(y-1)^2-0.1)=0 [-20, 20, -10, 10]}