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# Linear & nonlinear functions: missing value

Video transcript

Find the missing value to
make the table represent a linear equation. So let's see this
table right over here. So when x is equal
to 1, y is 3/2. When x is 2, y is equal to 3. So let's see what happened. When x increased by
1, what did y do? Well looks like y
increased by 3 and 1/2 is the same thing as 1 and 1/2. So to go from 1 and 1/2 to
3, it increased by 1 and 1/2, or you could say it
increased by 3/2. You could say that 3 is the
same thing as 6/2, 6/2 minus 3/2 is another 3/2. All right. Now when we go
from 2 to 3, we're increasing by 1 again in x. And what are we doing in y? So we're going from 3, which is
the same thing as 6/2 to 9/2. So once again, we are
increasing by 3/2. So in order for this
to be a linear equation or a linear relationship,
every time we increase by 1 in
the x direction, we need to increase by 3/2. If we increase by 2, we need
to increase by 2 times 3/2. So what are we doing over
here on this fourth term on the table? Well we're increasing. We're going from 3 to 8
so we are increasing by 5. So if we're increasing
x by 5, then we need to increase y by 5
times 3/2 or 15 over 2. So that's the amount that
we have to increase y by. If we started at 9/2 and we're
going to increase by 15/2, so it's going to
be 9/2 plus 15/2, this is how much
we increment by. Remember, we increment
3/2 every time x moves 1. This time, x moved 5. So we're incrementing
by 15/2, or you could say we're incrementing
by 3/2 five times. But this is going
to be equal to 9 plus 15 is 24 over 2
which is equal to 12. And so in the box, we could
write 12, and we are done.