How do you graph #\frac { 1} { 6} x - \frac { 1} { 2} y = - 1#?

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Answer 1 · 2018-01-15T13:45:04

See a solution process below:

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

First Point: For #x = 0#

#(1/6 * 0) - 1/2y = -1#

#0 - 1/2y = -1#

#-1/2y = -1#

#color(red)(-2) xx -1/2y = color(red)(-2) xx -1#

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

#1y = 2#

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

Second Point: For #y = 0#

#1/6x - (1/2 * 0) = -1#

#1/6x - 0 = -1#

#1/6x = -1#

#color(red)(6) xx 1/6x = color(red)(6) xx -1#

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

#1x = -6#

#x = -6# or #(-6, 0)#

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

graph{(x^2+(y-2)^2-0.075)((x+6)^2+y^2-0.075)=0 [-20, 20, -10, 10]}

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

graph{((1/6)x - (1/2)y + 1)(x^2+(y-2)^2-0.075)((x+6)^2+y^2-0.075)=0 [-20, 20, -10, 10]}