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Equations of a Line - Example 1

In mathematics, a line is a straight line segment with zero curvature. The most familiar types of lines are the lines in Euclidean geometry, which are described by two numerical parameters, and the lines in non-Euclidean geometry, which are described by more than two parameters.

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Okay, so let's go look at this example for the equation of a line word problem. So this one says Bob is baking cookies before he starts. He needs to pay for the mixer and the baking tray, which cost $40. Upon his calculations, he realizes that the cost of each cookie could be modeled in a linear fashion. The ingredient costs broken down for each cookie is 70 cents. What is the equation of the line that describes the total cost? Why, for the number of cookies X that Bob makes Okay, so let's go on to start out by thinking about how we know that this is actually gonna be, um, the equation of a line. Well, first of all, we do know that it says that the cost of each cookie could be modeled in a linear fashion. So this keyword linear right here tells us that it is gonna be why is equal to M X plus B? Okay. Another way to check, though, is to realize that all of these are in the form of why is equal to Mexico's to be so because all of your answer choices are in it, there's not really a way that it could be an exponential or anything like that because of the fact that it the all the answer choices are in the near form. So then let's check for the things that we need to check for. Well, we know that the two things are gonna be slope, which is R N value and B, which is our Y intercept value. So then we discussed the keywords that kind of represents slope. So something would be like SLOPE would be some sort of a raid or something for something. So then what we see here is that it says that the ingredient costs broken down for each cookie for each cookie. So that gives some sort of a rate, so that's gonna be 70 cents. So we know that that one has to be our slope. So then, by feeling that in, I'm going to get Y is equal to 0.70 x plus some B. So we still have to find RB. So then, for the B, we know that the B value is some sort of like a starting point initial value baseline fee, um, one time fee starting value. But regardless of what it is, it has to be some sort of either like a one time Onley payment or one time value or some sort of a starting value where did in slightly different ways. So we know that that kind of looks like this 1 40 because it says that before he starts so initially. Initially you need to pay for the mixer and the baking tray, which cost $40. So that's going to give us why is equal to 0.70 X plus the 40 Because that's just you do it once, and then you never have to use it again. You have to have to pay for it again, and you can use as many times as you want to make the cookies. So then that looks like answer choice. Be because we've got the 0.70 for the slope and the 40 for the intercept. So be is going to be our correct answer

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Ahyeon H.

University of California, Berkeley

Emma C.

Wellesley College

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Charles C.

Kennesaw State University

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Ball State University

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