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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.

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• 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??
• 500 meters divided by 4 hours (500 divided by 4) equals 125 meters divided by 1 hour, that means 125 m/hours
(1 vote)
• kinda confusing ngl, all of the questions i do don't have a starting point like 1200m how do i complete it then?
• You replace 1,200 with whatever the value is.
• 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.
• 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
(1 vote)
• What is the formula for this?
(1 vote)
• 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
• How do you find the Y-intercept if they give you the rate of change and one point?
• You can use the slope-intercept form, y = mx + b.

I'll use an example to help explain: The rate of change of a line is 3, it passes through the point (1, 5). Find the y-intercept of the line.

b = y-intercept, so we have to find b.

The rate of change = slope = m
Therefore sub m = 3:
y = 3x + b

Then sub the point (1, 5):
5 = 3(1) + b
2 = b

So the y-intercept is (0, 2).
• If an axis is given a variable other than x_ or _y, for example, t_, which stands for _time in Physics, will it be called the t-intercept?
• i do believe so but save that for when talking about time and stick with x and y so it is not confusing k
• Mr. Mole left his burrow that lies 7 meters below the ground and started digging his way deeper into the ground, descending at a constant rate. After 6 minutes, he was 16 meters below the ground.

Mr. Mole's burrow lies 7 meters below the ground. This corresponds to the point (0,−7), which is also the y-intercept.

After 6 minutes, Mr. Mole was 16 meters below the ground, which corresponds to the point (6,-16)

Let's use the slope formula with the points (0,-7) and (6,-16)

m= −16−(−7)/6-0 = -9/6 = -1.5

This means that Mr. Mole is descending at a rate of 1.51 meters per minute.

Now we know the slope of the line is −1.5 and the y-intercept is (0, -7), so we can write the equation of that line:

y=-1.5x-7

SO, how would I know how to use the slope formula thing, which number are supposed to go on top and go on the bottom?