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Plot the lines found in Exercise $13$.

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Missouri State University

Harvey Mudd College

Idaho State University

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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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 got in exercise. 13. So if you need to go back, look at 13. Refresh your memory. What? This equation is where it comes from. Thick way Zhishan is why equals 1/6 X. Okay, So what we have here, this equation is in, uh, slope intercept. Form the slope Intercept form. The name tells you exactly what to expect. The coefficient of my ex term is the slope of my line. The constant term is my wife intercept. Okay. Now, in this case, the white intercepted black. There is no constant, but what we can do, we could say that. That's plus zero. So our y intercept zero, which is actually the origin. Okay, so where do we start? We've got our equation. We know what the numbers mean. How do we graph it? Well, you always start with a point that you know for sure. A point that you know is gonna be on your line. That's gonna be our y intercept. So in this case, I had that plus zero. My line goes right through the origin, so I'm gonna put a green dot right at the origin on my grid. Now we're going to use this slope to place other points on our grid. So let's review what the slope is. Slope is rise over. Run. Rise. Is the change in your Y values how fast you're rising or falling as you go across with your line. Run. Is the change in X how fast you go? Side to side. Now, In this particular case, are Slope is 1/6. That means I will go up one unit to my rise for every six units I go across my run. One note before we go back to the grid. This is a positive slope, which means my line should be increasing. As I go from left to right, a positive slope will be trending upward. So we'll check at the end to make sure that airline matches that. Okay, starting at the point we know at the Y intercept at the origin. I'm gonna rise one and go over. 123456 And I'm gonna place a point up one, 45 and over six. If I want to go the other way to put in one more point, I can on 23456 I could put a point down there in the third quadrant. All those points line up on a nice straight line. We just connect the dots. If you're using pencil and paper, I recommend you use a ruler on graph paper if you can. Just helps you be a little more precise. Makes us a little bit easier to dio. Okay, so we have our equation and we have our graph. We started with the Y intercept. We then use the slope to play some more points, which we could then connect the dots and we can confirm that our slope is indeed going upward the way we expected it to.

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