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Plot the lines found in Exercise $11$.

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Oregon State University

McMaster University

Harvey Mudd College

Lectures

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In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Plot the lines found in Ex…

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for this problem. We've been asked to graft the equation that we got an exercise number 11. If you go back and do exercise 11, you'll see that our equation is why equals negative three X plus 11. If you don't know where that equation came from, take a pot pause this video, go back and look at exercise 11. Make sure you understand it. Then come back and we'll talk about how to graph the our equation. Okay, so what we have here, this equation is in slope intercept form. It's kind of a boring name, but it tells you exactly what we have that the coefficient in front of our X term is the slope of our line. And the constant, including the sign, is our Y intercept. Okay, when we start to graph a line, we need a starting point a point that we know for sure is gonna be on our line. So our starting point step number one is to graph the Y intercept point in this case. That's at 11. So I'm going to go up. 123456789 10, 11. I'm way up there at the top remember that Axis just keeps going. So there is my point. Yeah, now that I have a point, I can use my slope to find other points on my line that I can then connect. So let's review what slope is. Slope is rise overrun. Rise is my change and why it's how fast I rise or fall over a given time period. Run is the change in the X value, the change side to side. So in this case, that rise over run that slope is negative three. Now it can be tempting to say it doesn't have a run and there's no denominator. But don't forget. Every integer has a denominator of one. So this is a slope of negative 3/1. I'm going to rise a negative three, also called dropping, and then run one. Right now, let's put those on our point here before we do. Let's just take one quick other note here. Negative slope. Negative slope means I will be going downwards as I go from left to right across my grid. My line should be trending down. Let's make sure that we'll check that at the end to make sure it works Okay, So rise. I'm gonna drop three and run one. Drop three. Run one. As you can see, as I do this multiple times, those dots line up in a nice, neat, um, pattern here, and you can see that's a drop of 3/1 Drop of 3/1. Get rid of those little lines there. Okay, Now, the last thing we need to do is just connect the points. If you are doing this with pencil and paper, highly suggest you use a ruler and graph paper. If you have access to it. Just kind of make sure that you are biggest careful. It's possible. The more precise you are, the easier these kinds of problems are. Um, so I just would recommend that if you have that as an option. Okay, so in review, we started with our Y intercept using our slope, we were able determine a few other points on our line, and it does have a downward slope, just like we predicted.

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