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### Course: Pre-algebra > Unit 14

Lesson 6: Linear and nonlinear functions# Linear & nonlinear functions: word problem

Learn to determine if the relationship described in a word problem is a function. Created by Sal Khan.

## Want to join the conversation?

- y=mx+b is a slope form. We use this to tell if it is a function or not. If it follows the formula y=mx+b then you know that it is proportional.(12 votes)
- what would the linear equation be, if on a table the x value was 0, and the y value was 49, and the y value kept decreasing by -35 and the x value kept rising by 1.?(4 votes)
- I think that it would be: y=14x, and the y-intercept would be 0. The next two values in the table would be 14 and 1 because 49-35=14 and 0+1=1. Since 14 divided by 1 is still 14, the slope would be 14.(2 votes)

- is b the slope or initial value(2 votes)
- B is the y-intercept. that means where the line meets with the y-axis. you could also look at it like this. y=mx+b, if x equals 0 then m*0 is 0 then y would equal B. So B is the y-intercept(M is the slope).(2 votes)

- Say, (x) increases by 3 each time but what if (y) increased gradually. for example (x) goes, (1,3,6,9,12) and (y) went (4,5,7,10,14) would that be a linear or non-linear?(2 votes)
- It is definitely not linear, remember slope is (y2-y1)/(x2-x1) and this has to stay the same between any two points. The first two give (5-4)/(3-1)=1/2. The second and third give (7-5)/(6-3)=2/3 which are not the same.(2 votes)

- What's a non-linear example then?(1 vote)
- A eagle is diving into the water to catch a fish. He sees the fish when he is 20 feet above the water, he then dives to two feet below the surface and catches the fish, and 10 seconds after he started to dive he rose back to 20 feet. Find a quadratic equation which approximates the path the eagle travelled.(4 votes)

- These comments are wild...(2 votes)
- Why is he just know telling us this late in the course-x =-1x(1 vote)
- How do you solve this -9x power of 2 - 10x - 4(1 vote)
- y=mx+b is how we express slope in a equation(1 vote)
- y=mx+bis a slope form, that tell you weather its a fraction or not, it also tells you if it is a proportion or not(1 vote)

## Video transcript

Luis and Kate have two video
games they want to play. They plan to spend exactly 45
minutes playing the two games. They want to use an
equation to express the relationship between the
number of minutes they spend playing Super Bologna Man
and the number of minutes they spend playing You
Have to Cut the Wire. Can this relationship
be represented using a linear equation? So let's see if it can. Let's define one variable
for the amount of time, the number of minutes they
spend playing Super Bologna Man. Let's define that as, well
let's just say that's x. So x is equal to time
playing Bologna Man. I'll write Bologna right here. And let's define y as y is
equal to the number of minutes they spend playing You
Have to Cut the Wire. So it's time playing, I'll
just call it Wire for short. So if we have the
minutes they play time playing Bologna and the
time playing Cut Your Wire. If I were to add those two
together, so if I say x plus y. I'll write that plus in a
neutral color, x plus y. What does this need
to be equal to? The time I play Bologna
Man plus the time I play Have to Cut the Wire. Well if I add them
together, they want to spend exactly 45
minutes playing both games. So this is going to be
equal to 45 minutes. Now we have set up
an equation that relates the time playing
Bologna Man and the time playing You Have
to Cut the Wire. But now we have to think about
is this a linear relationship? So one way to think about
it is the real giveaway for a linear relationship
is if you can write it in the traditional
form of a line. So if you can write
it in the y is equal to mx plus b form, where
m is the slope of the line and b is the y-intercept. So let's see if we can do that. Well if we want to
do that here, we could just subtract
x from both sides. You subtract x from
both sides, you get-- so let's
subtract an x over here, let's subtract
an x over here. So negative x plus this and
then subtract an x there. Well, that's going
to cancel, and you're going to be left
with-- and I'm going try to write it in this
form right over here-- y is equal to 45. Let me do that in
the same color, just to make it not be confusing. y is equal to, and I'll
write the negative x first because we have the x term
right over here first. So y is equal to
negative x plus 45. All I did is I switched
these two terms around. But you see here,
it has that form. And you might say
wait what is m here? I see that b is 45. Well if I write
negative x, that's the same thing as
writing negative 1x. So this is definitely a line. I was able to write it in
this form right over here. So can this relationship
be represented using a linear equation? Absolutely, absolutely yes.