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### Course: Operations and Algebraic Thinking 229+ > Unit 3

Lesson 1: Intro to slope-intercept form# Constructing linear equations from context

Given a written description of a linear relationship in a some context, write an equation that represents the linear relationship described.

## Want to join the conversation?

- I've redone this segment at least 10 times and everyday I redo it I don't get any closer to figuring it out, the word problems are so confusing. I understand what I'm supposed to do but I can't seem to determine what value goes to what.(48 votes)
- I also had to do it many times before mastering it. My advice to you for this exercise is that you should first be proficient with all the forms of linear equations. Once you've done that. read the question and think-which form should be used here?

For example, if only the slope and y-intercept is given you'll have to use the slope-intercept form.

Also, this exercise demands the ability to convert verbal information into mathematical form. For example, the rate with which Mr.Mole digs is the*slope*of the line and the initial depth of his burrow will be the y-intercept.

Finally, don't give up! All these times you've attempted the exercise, you've been developing your brain. You can learn anything!(22 votes)

- This problem is not even close to the ones that I encounter:

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After 11 months, he weighed 140 kilograms. He gained weight at a rate of 5.5 kilograms per month.

Like how does this relate to the video at all?(18 votes)- The sumo wrestler in that question is gaining weight at a constant ratio. Linear equations have slopes that do not change throughout the function, just like his rate of gaining weight. Like @hiroto.honda said, you find the y-intercept and slope to construct a linear equation. The slope is already given (rate at which he is gaining weight). So all you need to do is find the y-intercept and plug it into the form y=mx+b as b.

Hope this helps(6 votes)

- How does he get 125 m/hours??(10 votes)
- 500 meters divided by 4 hours (500 divided by 4) equals 125 meters divided by 1 hour, that means 125 m/hours(5 votes)

- I never understand why the use such an easy word problem for the videos/teaching then the test comes and the word problems are like ten times harder..(12 votes)
- XD your bio made me laugh. Love it!(6 votes)

- kinda confusing ngl, all of the questions i do don't have a starting point like 1200m how do i complete it then?(11 votes)
- You replace 1,200 with whatever the value is.(5 votes)

- I'm stuck on this :/

Addison painted her room. She had 50 square meters to paint, and she painted at a constant rate. After 2 hours of painting, she had 35 square meters left.

Let y represent the area (in square meters) left to paint after x hours.(8 votes) - I've redone this segment at least 10 times and everyday I redo it I don't get any closer to figuring it out, the word problems are so confusing. I understand what I'm supposed to do but I can't seem to determine what value goes to what.(8 votes)
- How can I feel less overwhelmed by looking at word problems? I always skip them.(4 votes)
- The first thing to do generally is to define your variables if the word problem does not define them for you. Then, you need to learn your vocabulary to tell what operations, parentheses, and where the equal goes (= are usually verbs in word problems). You can find some practice if you look up Kuda pre-algebra or algebra and find the worksheets on word problems or other sites.(4 votes)

- Can someone please explain this in short, I find it hard to understand so if someone could help it would be great! I have tried it A LOT of times and still don't get it.(3 votes)
- there are two things you need to know. you are trying to find the function y = mx + b. you want m and b.

m is the slope and b is the y intercept.

For this problem the function is looking at elevation per time. Specifically meters per hour. if you have two points you can find the slope with the formula (y2 - y1)/(x2 - x1) where two points are (x1, y1) and (x2, y2). It doesn't matter which you make point and 2.

The two points it gives are time = 0 at 1200 meters and time = 4 hours 1700 meters, so the points are (0, 1200) and (4, 1700) so let's go ahead and find the slope.

(y2 - y1)/(x2 - x1) where (x1, y1) = (0, 1200) and (x2, y2) = (4, 1700)

(1700 - 1200)/(4 - 0)

500/4

125

so the slope m = 125

now the y intercept. the y intercept is when x = 0. But hey, we know the point where x = 0, so we know the y intercept. b = 1200

so now we can fill in y = mx + b

y = 125x + 1200

Hope this helps!

Calc-You-Later!(5 votes)

- What is the formula for this?(2 votes)
- there are two things you need to know. you are trying to find the function y = mx + b. you want m and b.

m is the slope and b is the y intercept.

For this problem the function is looking at elevation per time. Specifically meters per hour. if you have two points you can find the slope with the formula (y2 - y1)/(x2 - x1) where two points are (x1, y1) and (x2, y2). It doesn't matter which you make point and 2.

The two points it gives are time = 0 at 1200 meters and time = 4 hours 1700 meters, so the points are (0, 1200) and (4, 1700) so let's go ahead and find the slope.

(y2 - y1)/(x2 - x1) where (x1, y1) = (0, 1200) and (x2, y2) = (4, 1700)

(1700 - 1200)/(4 - 0)

500/4

125

so the slope m = 125

now the y intercept. the y intercept is when x = 0. But hey, we know the point where x = 0, so we know the y intercept. b = 1200

so now we can fill in y = mx + b

y = 125x + 1200(7 votes)

## Video transcript

- [Instructor] Tara was
hiking up a mountain. She started her hike at an
elevation of 1,200 meters and ascended at a constant rate. After four hours, she reached
an elevation of 1,700 meters. Let y represent Tara's elevation
in meters after x hours. And they ask us, and this is from an exercise on Khan Academy, it says, complete the equation for the relationship between the elevation
and the number of hours. And if you're on Khan
Academy, you would type it in, but we can do it by hand. So pause this video and
work it out on some paper and let's see if we get to the same place. All right, now let's do this together. So first of all, they tell us that she's ascending at a constant rate. So that's a pretty good indication that we could describe her elevation based on the number of hours she travels with a linear equation. And we could even figure
out that constant rate. It says that she goes from 1,200 meters to 1,700 meters in four hours. So we could say her rate is going to be her change in elevation over a change in time. So her change in elevation is 1,700 meters minus 1,200 meters and she
does this over four hours. Over, her change in time is four hours. So her constant rate
in the numerator here, 1,700 minus 1,200 is 500 meters. She's able to go up 500
meters in four hours. If we divide 500 by four, this is 125 meters per hour. And so we could use this now to think about what our equation would be. Our elevation y would be equal to, well, where is she starting? Well, it's starting at 1,200 meters. So she's starting at 1,200 meters. And then to that, we're going to add how much she climbs based on
how many hours she's traveled. So it's going to be this rate, 125 meters per hour times the number of hours she has been hiking. So the number of hours is x times x. So this right over here is an equation for the relationship between the elevation and the number of hours. Another way you could
have thought about it, you could have said, okay, this is going to be a linear equation because she's ascending
at a constant rate. You could say the slope intercept form for a linear equation is
y is equal to mx plus b, where b is your y-intercept. What is the value of y
when x is equal to zero? And you'd say, all right, when x is equal to zero, she's at an elevation of 1,200. And then m is our slope. So that's the rate at which
our elevation is increasing. And that's what we
calculated right over here. Our slope is 125 meters per hour. So notice, these are equivalent. I just have, these two terms are swapped. So we could either write
y is equal to 1,200 plus 125x or you could write
it the other way around. You could write 125x plus 1,200. They are equivalent.