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## Algebra 1

### Course: Algebra 1>Unit 5

Lesson 3: Writing slope-intercept equations

# 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. • 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!
• How does he get 125 m/hours?? • 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? • 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
• kinda confusing ngl, all of the questions i do don't have a starting point like 1200m how do i complete it then? • 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. • 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. • How can I feel less overwhelmed by looking at word problems? I always skip them. • 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.
• 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. • 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!
• What is the formula for this? • 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 