How do you graph #4x=2y+6# using the x and y intercepts?

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Answer 1 · 2017-11-09T16:00:57

See a solution process below:

First, we need to determine the #x# and #y# intercepts.

x-intercept

Set #y# equal to #0# and solve for #x#:

#4x = (2 * 0) + 6#

#4x = 0 + 6#

#4x = 6#

#(4x)/color(red)(4) = 6/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 3/2#

#x = 3/2#

#(3/2, 0)#

x-intercept

Set #x# equal to #0# and solve for #y#:

#4 * 0 = 2y + 6#

#0 = 2y + 6#

#0 - color(red)(6) = 2y + 6 - color(red)(6)#

#-6 = 2y + 0#

#-6 = 2y#

#-6/color(red)(2) = (2y)/color(red)(2)#

#-3 = (color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2))#

#-3 = y#

#(0, -3)#

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

graph{(x^2+(y+3)^2-0.025)((x-(3/2))^2+y^2-0.025)=0 [-10, 10, -5, 5]}

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

graph{(4x-2y-6)(x^2+(y+3)^2-0.025)((x-(3/2))^2+y^2-0.025)=0 [-10, 10, -5, 5]}