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How do you find the #x# and #y#-intercept for the equation: 4x - 3y - 6 = 0#?

Answer 1

Julia Adams

See a solution process below:

x-intercept: Set #y# to #0# and solve for #x#:

#4x - 3y - 6 = 0# becomes:

#4x - (3 * 0) - 6 = 0#

#4x - 0 - 6 = 0#

#4x - 6 = 0#

#4x - 6 + color(red)(6) = 0 + color(red)(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)) = 6/4#

#x = 3/2#

The x-intercept is: #x = 3/2# or #(3/2, 0)#

y-intercept: Set #x# to #0# and solve for #y#:

#4x - 3y - 6 = 0# becomes:

#(4 * 0) - 3y - 6 = 0#

#0 - 3y - 6 = 0#

#-3y - 6 = 0#

#-3y - 6 + color(red)(6) = 0 + color(red)(6)#

#-3y - 0 = 6#

#-3y = 6#

#(-3y)/color(red)(-3) = 6/color(red)(-3)#

#(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = 6/-3#

#y = -2#

The y-intercept is: #y = -2# or #(0, -2)#

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Answer 2

Ethan Adkins

To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.