Transcription
Some ordered pairs for a linear function of x are given in the table below. Which equation was used to generate this table? So they give us a bunch of data points. When x is 4, y is negative 8. When x is 7, y is negative 20, so on and so forth. And these points have been generated by one of these equations right over here, so let's just see which of these equations actually could have generated all of these points.
So let's go to this first point right over here, 4, -8, and let's go equation by equation. If x is 4 here, -2 times 4 would be -8. Let me just write it down. We'd multiply -2 times 4 to get -8, and then I would add 1 to get -7. I would get -7. So for this equation, when x is 4, y would be -7, not -8. So this equation definitely did not generate this top point right over here. So we could just rule it out. Whatever equation should have been able to generate for any given x, for any of these x's, should generate this y right over here.
Now let's go to this next equation: y = -2x + 0. So when x is 4, y would be -2 times 4, which is -8. So this second equation seems to be capable of generating this first set of points. When x is 4, y is -8. But let's see if it works for this second one right over here. When x is 7, you would have -2 times 7, which is -14, but here, when x is 7, y is -20. So this one, we can rule out, because when x is 7, y does not equal -20 like this point right over here. So we'll rule that second one out.
Now let's look at this third one: y = -4x + 8. Well, we could go to this first point again. When x is 4, let's think about what happens when x is 4. So when x is 4, you have -4 times 4, which is -16, plus 8, which is -8. So it seems to be able to generate this first point. When x is 4, y is -8 for this equation right over here. Now let's see what happens when x is 7. So -4 times 7 is -28. -28 + 8 is -20, so this candidate is starting to look pretty good. It's pretty good. It satisfies these two points, and frankly, for any of these linear functions, if it satisfies any of these two points, if some linear function generated all of these, if some function can generate any two of them, it will satisfy all of these, because two points define a line. But we can verify it right over here.
So let's see what happens when x = 8. -4 times 8 is -32, plus 8 is -24. So that satisfies so that when x is 8, y does equal -24. And then finally, let's look at that last point. When x is 9, -4 times 9 is -36, plus 8 is equal to -28. And that's exactly what we see here in this table. So we don't even have to look any further. Choice 3 satisfies the conditions that when x is any one of these things, the corresponding y that's defined by this equation is going to be when x is 4, y is -8. When x is 7, y is -20, so on and so forth.