What is the #y#-intercept of the line #2x-3y = -6#?

2 Answers
David G.
Jan 31, 2016

The y-intercept is the point on the y-axis where the line crosses. The y-axis is the line #x=0#, so substitute in #0# for #x# and solve. The y-intercept is #y=2#.

Explanation:

The y-axis is the line #x=0#. Substitute in #0# for #x# in the equation to find the y-intercept:

#2x-3y=-6#

#2(0)-3y=-6#

#-3y=-6#

#y=(-6)/-3 = 2#

The y-intercept is simply #y=2#.

Rachel
Jan 31, 2016

The answer is, in coordinate-pair format: #(0, 2)#

Explanation:

The #y#-intercept is the value of #y# when #x=0#.

That means to solve this we should replace #x# with #0# and solve for #y#.

Now the equation looks lie this #2(0)-3y=-6#.
From here, I would solve #2x*0#, which is #0#. The equation is now #-3y=-6#, and from here I would divide both sides by #-3#. The updated version of the equation is #y=-6/-3#,or #y=2#.

We can also graph the equation and check where the #y#-intercept is.

graph{-6=2x-3y}
In this case, it is at (0, 2), which is what we found. We were right!

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