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

Lesson 2: Linear equations word problems

# Linear equation word problems

Linear equation word problems.

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• i still don't get it, how do you find what t is?
• 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)
• it is too confusing! I don't get it still!
• That really does help. thanks. happy Easter to you too!
• i am still not understanding how he got this answer
• 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
• This is confusing... Anyone get it? :/
• 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
8+15 is 23, so the answer is 23 degrees celsius
• I'm very confused! I don't know how to do this!
• 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.
• This is much easyer than the last quiz
• I don't get it.
How do we solve Q=15+0.4t?
• 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.