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Studying for a test? Prepare with these 4 lessons on Module 4: Linear equations.

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# Testing solutions to linear equations

Video transcript

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 comma negative 8, and let's
go equation by equation. If x is 4 here, negative 2
times 4 would be negative 8. Let me just write it down. We'd multiply negative 2
times 4 to get negative 8, and then I would add
1 to get negative 7. I would get negative 7. So for this equation,
when x is 4, y would be negative
7, not negative 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 is equal to
negative 2x plus 0. So when x is 4, y would
be negative 2 times 4, which is negative 8. So this second
equation seems to be capable of generating
this first set of points. When x is 4, y is negative 8. But let's see if it
works for this second one right over here. When x is 7, you
would have negative 2 times 7, which is negative
14, but here, when x is 7, y is negative 20. So this one, we can rule
out, because when x is 7, y does not equal negative
20 like this point right over here. So we'll rule that
second one out. Now let's look at
this third one. y is equal to
negative 4x plus 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 negative 4 times 4, which is negative 16,
plus 8, which is negative 8. So it seems to be able to
generate this first point. When x is 4, y is negative 8 for
this equation right over here. Now let's see what
happens when x is 7. So negative 4 times
7 is negative 28. Negative 28 plus
8 is negative 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 equals 8. Negative 4 times 8 is negative
32, plus 8 is negative 24. So that satisfies so that when x
is 8, y does equal negative 24. And then finally, let's
look at that last point. When x is 9, negative 4
times 9 is negative 36, plus 8 is equal to negative 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 negative 8. When x is 7, y is negative
20, so on and so forth.