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We're told to find the x- and y-intercepts for the graph of

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this equation: 2 y plus 1/3x is equal to 12.

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And just as a bit of a refresher, the x-intercept is

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the point on the graph that intersects the x-axis.

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So we're not above or below the x-axis, so our y value

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must be equal to 0.

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And by the exact same argument, the y-intercept

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occurs when we're not to the right or the left of the

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y-axis, so that's when x is equal to 0.

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So let's set each of these values to 0 and then solve for

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what the other one has to be at that point.

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So for the x-intercept, when y is equal to

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0, let's solve this.

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So we get 2 times 0, plus 1/3x is equal to 12.

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I just set y is equal to 0 right there, right?

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I put 0 for y.

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Well, anything times 0 is just 0, so you're just left with

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1/3x is equal to 12.

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To solve for x, you can think of it as either dividing both

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sides by 1/3, or we can multiply both sides by the

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reciprocal of 1/3.

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And the reciprocal of 1/3 is 3, or you can even think of it

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as 3 over 1.

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So times 3 over 1.

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And so we're left with 3 times 1/3, that just cancels out, so

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you're left with x is equal to 12 times 3, or

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x is equal to 36.

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So when y is equal to 0, x is 36.

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So the point 36 comma 0 is on the graph of this equation.

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And this is also the x-intercept.

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Now, let's do the same thing for the y-intercept.

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So let's set x equal 0, so you get 2y plus 1/3, times 0 is

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equal to 12.

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Once again, anything times 0 is 0.

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So that's 0, and you're just left with 2y is equal to 12.

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Divide both sides by 2 to solve for y, and you're left

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with y is equal to 12 over 2, is 6.

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So the y-intercept is when x is equal to 0 and

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y is equal to 6.

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So let's plot these two points.

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I'll just do a little hand-drawn graph, and make it

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clear what the x- and the y-intercepts are.

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So let me draw-- that's my vertical axis, and that is my

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horizontal axis-- and we have the point 36 comma 0.

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So this is the origin right here, that's the x-axis,

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that's the y-axis.

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The point 36 comma 0 might be all the way over here.

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So that's the point 36 comma 0.

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And if that's 36, then the point 0, 6 might be right

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about there.

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So that's the point 0, 6.

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And the line will look something like this.

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I'm trying my best to draw a straight line.

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And notice where the line intercepted or intersected the

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y-axis, that's the y-intercept, x is 0, because

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we're not to the right or the left of it.

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Where the line intersected the x-axis, y is 0, because we're

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not above or below it.

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