Transcription
We're told to find the x- and y-intercepts for the graph of this equation: 2y + 1/3x = 12.
And just as a bit of a refresher, the x-intercept is the point on the graph that intersects the x-axis. So we're not above or below the x-axis, so our y value must be equal to 0. And by the exact same argument, the y-intercept occurs when we're not to the right or the left of the y-axis, so that's when x is equal to 0.
So let's set each of these values to 0 and then solve for what the other one has to be at that point. So for the x-intercept, when y = 0, let's solve this. So we get 2 * 0 + 1/3x = 12. I just set y = 0 right there, right? I put 0 for y. Well, anything times 0 is just 0, so you're just left with 1/3x = 12. To solve for x, you can think of it as either dividing both sides by 1/3, or we can multiply both sides by the reciprocal of 1/3. And the reciprocal of 1/3 is 3, or you can even think of it as 3/1. So * 3/1. And so we're left with 3 * 1/3, that just cancels out, so you're left with x = 12 * 3, or x = 36. So when y = 0, x = 36. So the point (36, 0) is on the graph of this equation. And this is also the x-intercept.
Now, let's do the same thing for the y-intercept. So let's set x = 0, so you get 2y + 1/3 * 0 = 12. Once again, anything times 0 is 0. So that's 0, and you're just left with 2y = 12. Divide both sides by 2 to solve for y, and you're left with y = 12/2 = 6. So the y-intercept is when x = 0 and y = 6.
So let's plot these two points. I'll just do a little hand-drawn graph, and make it clear what the x- and the y-intercepts are. So let me draw-- that's my vertical axis, and that is my horizontal axis-- and we have the point (36, 0). So this is the origin right here, that's the x-axis, that's the y-axis. The point (36, 0) might be all the way over here. So that's the point (36, 0). And if that's 36, then the point (0, 6) might be right about there. So that's the point (0, 6). And the line will look something like this. I'm trying my best to draw a straight line. And notice where the line intercepted or intersected the y-axis, that's the y-intercept, x = 0, because we're not to the right or the left of it. Where the line intersected the x-axis, y = 0, because we're not above or below it.