How do you graph #\frac { 1} { 3} x - \frac { 1} { 7} y = - 1#?

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Answer 1 · 2018-01-15T13:22:07

See a solution process below:

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

First Point: For #x = 0#

#(1/3 * 0) - 1/7y = -1#

#0 - 1/7y = -1#

#-1/7y = -1#

#color(red)(-7) xx -1/7y = color(red)(-7) xx -1#

#color(red)(7)/7y = 7#

#1y = 7#

#y = 7# or #(0, 7)#

Second Point: For #y = 0#

#1/3x - (1/7 xx 0) = -1#

#1/3x - 0 = -1#

#1/3x = -1#

#color(red)(3) xx 1/3x = color(red)(3) xx -1#

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

#1x = -3#

#x = -3# or #(-3, 0)#

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

graph{(x^2+(y-7)^2-0.075)((x+3)^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{((1/3)x - (1/7)y + 1)(x^2+(y-7)^2-0.075)((x+3)^2+y^2-0.075)=0 [-20, 20, -10, 10]}