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Plot the lines found in Exercise $9$.

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:43

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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02:47

Plot the lines found in Ex…

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Find the equations of the …

for this problem. We've been asked to graft the equation that we found an exercise number nine. If you go back to exercise number nine, you'll see that the equation we ended up with was Why equals negative 13/47 X minus 112 over 47. Now, if you don't know where this equation came from, go back and review exercise nine. Take a break from this video. Make sure you understand the equation, then come back and we'll see about graphing it. So when we go to Grafton equation, remember that this equation is in slope intercept form. That means that the coefficient of the X term is the slope of our line. And the constant term, including the sign in front of it, is the Y intercept slope intercept form. When we go to graph, the first thing we need is a starting point. Where do we begin? Our line where we begin is with the Y intercept. So I'm going to graph that on my Y axis. Now, this is not a very nice neat number. 112 over 47 is approximately equal to 2.38 And these were negative. So I'll make those negative numbers. So negative. 2.38 I'm doing This is an approximate here. Uh, it's gonna be about where that green dot is. Now, my slope. Let's recall what slope is slope is. Rise over. Run. In other words, rise. That's the change in our Y values. How fast? Um, I rising or falling and run is the change And why That's the change. Side to side. I'm sorry. That's a change in X rises. The change in why run is the change in X In this case, that changes negative 13/47. Okay. And negative slope means it's going down eso as I go from left to right, my line will be trending downward. Now, What we traditionally do in for a slope is I go to my starting point, which is my y intercept. And I would drop 13 and go over 47. That's my rise over Run. My graph here is not large enough to count 13 and 47 had put me well off my grid. Eso What I'm going to say is this this is very close. If I did the decimal approximation of this 0.277 which is just a little bit bigger against the negative. Put a negative. They're just a little bit bigger than negative. 1/4 1/4 to be 13/52. We have 13/47. So if I do approximately down one and over four down one and over four, this is not perfect. But it's a good sketch. If you want to see a really good approximation of this, um, you could go into a graphic application of graphic calculator and it would be precise, but it's going to be very close to this. So I've got a couple of points here. We're just going to connect them. If you're doing this with pencil and paper. Using a ruler and graph paper is a great idea. You could be as precise as you can be. Um, get a nice, clean, straight line there. So this line has our approximate slope and our approximate why intercept. And this line does have that negative slope that we're expecting

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