How do you graph #15x+6y=-51#?

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Answer 1 · 2018-05-29T12:47:37

See a solution process below:

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

First Point: For #x = -3#

#(15 * -3) + 6y = -51#

#-45 + 6y = -51#

#-45 + color(red)(45) + 6y = -51 + color(red)(45)#

#0 + 6y = -6#

#6y = -6#

#(6y)/color(red)(6) = -6/color(red)(6)#

#y = -1# or #(-3, -1)#

Second Point: For #y = -6#

#15x + (6 * -6) = -51#

#15x + (-36) = -51#

#15x - 36 = -51#

#15x - 36 + color(red)(36) = -51 + color(red)(36)#

#15x - 0 = -15#

#15x = -15#

#(15x)/color(red)(15) = -15/color(red)(15)#

#x = -1# or #(-1, -6)#

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

graph{((x+3)^2+(y+1)^2-0.1)((x+1)^2+(y+6)^2-0.1)=0 [-20, 20, -10, 10]}

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

graph{(15x+6y+51)((x+3)^2+(y+1)^2-0.1)((x+1)^2+(y+6)^2-0.1)=0 [-20, 20, -10, 10]}