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Find the equations of the lines and plot the lines from Exercise $52$.

$y=1 / 2 x+3$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Missouri State University

Baylor University

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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Find the equations of the …

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Plot the points and find t…

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Plot the pair of points an…

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Plot each pair of points a…

for this problem, we're going to be referencing exercise number 52 from earlier in this lesson. So let's review what exercise 52 told us in that exercise we had two points 03 and negative 60 And in that exercise we found the slope of the line connecting them. We found that slope to be one half. So for this exercise, we want to find the equation of the line that this describes and then we're going to graph it. Now we have to traditionally, with two different ways that we would write the equation. We could put this into slope intercept, for I know myself one half, but let's keep it generic M X plus B or we could do point slope form. Why? Minus y one equals M times X minus X one slope intercept form is helpful to graph, and that is the form we're going to be putting it into eventually. But if I didn't have the y intercept, I couldn't use that form. Now just so happens I do have the y intercept so I can use the slope intercept form. I could say why equals my slope is one half and the B is three. So there's my equation. But what if I wasn't given that? Why intercepted? That's just luck of the draw that one of our points is the Y intercept. Let's look at the other one. We're just gonna show that we get the same answer no matter which format we use. So let's use the second point, and we're gonna use our slope a point slope form. That's why minus the Y coordinate, which is zero by slope is one half. I have X minus the x coordinate. So X minus negative six, which is equivalent to X plus six. If I get rid of those parentheses, I have one half X plus three so you can see it doesn't matter which way we go. We'll get the same answer in the end. Okay, Now let's graph this point or this line. Either case, um, you can see that are why intercept is going to be three. So I'll put that dot right there, and my slope is one half positive slope means my line will be trending upward as I go from left to right. And remember, slope his rise over run. So I'm going to go up one unit and over to up, 1/2 up, one over to, and I could do that and put several dots on that line If I want to, I could go the other direction as well, and I'm just going to connect thes points. So that's the graph of the line. Why equals one half X plus three?

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