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## Get ready for AP® Calculus

### Course: Get ready for AP® Calculus > Unit 4

Lesson 2: Linear equations word problems# Linear equation word problems

CCSS.Math:

Linear equation word problems.

## Want to join the conversation?

- i still don't get it, how do you find what t is?(26 votes)
- If t is minutes

Q=15+0.4t

my understanding is if he wants to know much the temperature increases with each (1) minute then:

Q=15+0.4(1)(15 votes)

- it is too confusing! I don't get it still!(21 votes)
- That really does help. thanks. happy Easter to you too!(4 votes)

- i am still not understanding how he got this answer(10 votes)
- t is an independent variable and the value of the whole equation(Q = 15 + 0.4t) depends on it. As t is a variable it can have any value. But we know that when Quinn returns home no time has elapsed yet. So, t becomes 0. Now that we know the value of t we just have to put it in the equation and we will get our answer.

Q= 15 + 0.4t

now, t=0

so, Q= 15 +0.4(0)

which is nothing but Q=15

hope this helps(8 votes)

- This is confusing... Anyone get it? :/(4 votes)
- Hi Rossy!

We are given the information of the y-intercept and slope. The formula for a linear equation is: y=mx +b in this case Y is replaced by Q. M is the slope and x is the constant so mx is .4t. Since he just came home his starting temperature (the y-intercept.) Since .4 is the slope that is the constant rate the temperature increases.T is a variable that we can use to plug numbers into.

So now that we have the equation and understand the y-intercept and slope, let's use the formula.

We are asked to find out how much the temperature will increase. So we will use our equation: Q=.4t + 15

To find the answer plug in 20 as the constant next to the slope and solve the equation.

Q= .4(20) + 15

-Multiply .4 times 20, which is 8

-Add 8 to 15

8+15 is 23, so the answer is 23 degrees celsius(3 votes)

- cheerleading is not a sport(5 votes)
- I don't get it.

How do we solve Q=15+0.4t?(4 votes)- You cannot solve it since it is already in slope intercept form. You can only solve for specific values (like creating a table), so when t=0, Q=15, when t=1, Q=15.4, when t=2, Q=15.8, etc.(2 votes)

- I'm very confused! I don't know how to do this!(3 votes)
- All Sal is doing in this video is finding the key features of a linear equation given in slope intercept (almost) form y=mx+b. Given Q=15+0.4t, we can switch to slope intercept form by moving right side to Q=0.4t+15 noting the y is represented by Q and x is represented by t. The slope is 0.4 and the y intercept is 15. There are many words that indicate the y intercept, beginning value, starting value, initial value, or similar terms such as temperature when he returned from vacation. Slope is also called rate of change which is worded how much does it change per minute (rate is temp/min) which has the "y" axis as temperature and the "x" axi is minutes. You rise .4 in temp for each run of 1 minute. To find the temperature after x minutes, you are just substituting a given value of the independent variable to solve for the dependent variable (or on a graph, you would find 20 minutes on the x axis, go up to the line, then over to the temperature). All you have to practice is learning vocabulary from word problems.(4 votes)

- Ok so this video doesn't explain everything about linear equation word problems very well. They left a lot out, and now I'm doing my practice tests and I'm completely stumped. Could I have some help?(3 votes)
- same here I was doing practice questions and I was confused.(3 votes)

- hi what if theyrs a fraction(4 votes)
- I don't get how to find the y-intercept one, it confuses me.(3 votes)
- Its a bit late for me to post this, but the y- intercept can be found in a number of ways. When we use graphs, we usually use the equation y=mx+b. B is our y- intercept in this. If you pause the video around1:08, you will see him writing this equation and explaining this. And for those that don't know, in the equation y=mx+b, mx is our slope and b is our y-intercept.(0 votes)

## Video transcript

- [Instructor] When Quinn
returned from vacation, he turned the heat back on in his home. He set the temperature
as high as it could go. Q represents the
temperature in Quinn's home in degrees Celsius after t minutes. This Q is equal to 15 plus 0.4t. What was the temperature when
Quinn returned from vacation? So pause this video and see if you can work
this out on your own. All right, so they wanna
know the temperature and you might get a little confused, hey maybe t is for temperature. No, t is time in minutes. Temperature is Q. Q represents the temperature. So they really wanna know is, what was Q when Quinn
returned from vacation? Well, right when Quinn
returned from vacation, that is when t is equal to zero. So this is equivalent to saying, what is Q, our temperature,
when zero minutes have elapsed? Well, if you go back to
this original equation, we see that Q is equal to 15 plus 0.4 times the amount
of elapsed time in minutes. So that's times zero. So that's just going to
be 15 degrees Celsius. If you're familiar with
slope intercept form, you could think of it as our temperature is equal to 0.4 times
the elapsed time plus 15. So t equals zero, you're
left with just this term which in many cases we
view as our y-intercept. What is going on right when
we're just getting started? Right when our horizontal
variable is equal to zero. And our horizontal variable in this situation is elapsed time. How much do the temperature
increase every minute? There's a couple of ways
you can think about this. One if you recognize, this
is slope intercept form. You could see that 0.4 is the slope. So that says for every one minute change in time, you're going to have an
increase in temperature by 0.4 degrees Celsius. So you could do it that way. You could try out some values. You could say, all
right, let me think about what Q is going to be based on t. So time, t equals zero
right when you got home. We're to figure out that the temperature
is 15 degrees Celsius. At t equals one, what happens? It's going to be 15 plus 0.4 times one. That's just gonna be 15.4. Notice, when we increased our time by one, our temperature increased
by 0.4 degrees Celsius by the slope. And what happened again
if we increased time by another minute, if
we go from one to two, we would get two, 15.8. We would increase
temperature by another 0.4. How much will the temperature increase if Quinn leaves the
heat on for 20 minutes? Pause the video and see
if you can solve that. All right, now we have to be careful here. They're not asking us what is the temperature after 20 minutes. They're saying, how much
will the temperature increase if he leaves the heat on for 20 minutes? If we just wanna know
what is the temperature after 20 minutes, we would just say, okay, what is Q when t is equal to 20? So it'd be 15 plus 0.4 times 20. 0.4 times 20 is eight. Eight plus 15 is 23. So it's 23 degrees
Celsius after 20 minutes. But that's not what they're asking us. They're asking, how much will
the temperature increase? Well, where did we start from? We started from 15 degrees Celsius and now after 20 minutes we
have gone to 23 degrees Celsius. So we have increased by
eight degrees Celsius. Or, another way to think about it, we have increased by this
amount right over here. We started at 15 and after 20 minutes, we have increased by 0.4 times 20 which is eight degrees Celsius. We're done!