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Plot the lines found in Exercise $15$.

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

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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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Find the equations of the …

this problem is asking us toe graph the equation that we got from exercise number 15. If you need to go back and review exercise 15 to see where what equation we're talking about, where we got it from. You could go ahead and pause this video, look at exercise 15 and then come back. Okay. From exercise 15. We ended up with the equation. Why? Equals 4.1 X minus 12.3. Okay, this equation is in slope intercept form. Now. The name of this form is very nice. It tells you exactly what to expect. The coefficient of R X term is the slope of our line. And the constant, including the sign, is the y intercept. Hence the name slope intercept form. Okay, we have our equation. We know what the numbers mean. Now, let's begin to graph. To start with, we need a point that we know for sure is on the line someplace where we could begin. That's going to be our Y intercept. So the first thing we're gonna do is we're gonna graph the y intercept onto our grid. So that's negative. 12.3. So let me count down 12 123456789 10, 11, 12.3 We're actually down about where that green dot is. Okay, So quite far down. Once I have a reference point to begin with that, Why intercept? I'll then go onto the slope. So let's review what slope is Slope is. Rise over. Run rises. My change in Why? How fast? Um, I rising or falling? Run. Is the change in X How fast is my line moving from side to side. Now, in this case, my rise over run is 4.1. So I could think of that is rising four and just a hair more every time I go one across if I want to be very precise And I had a nice big graph paper, I could multiply top and bottom by 10 and actually rise 41 go over 10. Uh, I'm gonna be doing this. This is a close enough approximation for what I have here. So let's come back over to our actually, before we come back over to our grid. We have a positive slope. Positive slopes mean that the line is increasing. So as we go left to right across our grid. Our lines should be trending upward. So we'll double check at the end to make sure that that's what happened. Okay, Slope of 4.1. So I'm going to go up. 1234 and just a little bit more. And go over one. Go up. 1234 Just a little bit more. And over 11234 Just a little bit more over one. Okay. So as you can see, as we go up on those points, we just connect those dots. I recommend using a ruler. If you have one on graph paper, if you have it, the more precise you are, the easier this kind of a job is. So we started with our Y intercept. We use the slope to find other points on our line. And it does indeed go upward the way we expected it to

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