How do you graph #2x - 3y = 9# using x- and y- intercepts?

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Answer 1 · 2018-03-19T22:54:54

See a solution process below:

First, find the y-intercept: Set #x = 0# and solve for #y#:

#(2 * 0) - 3y = 9#

#0 - 3y = 9#

#-3y = 9#

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

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

Next, find the x-intercept: Set #y = 0# and solve for #x#:

#2x - (3 * 0) = 9#

#2x - 0 = 9#

#2x = 9#

#(2x)/color(red)(2) = 9/color(red)(2)#

#x = 9/2# or #(9/2, 0)#

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

graph{(x^2+(y+3)^2-0.075)((x-(9/2))^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{(2x - 3y - 9)(x^2+(y+3)^2-0.075)((x-(9/2))^2+y^2-0.075)=0 [-20, 20, -10, 10]}