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Find the equations of the lines and plot the lines from Exercise $57$.

$x=1 / 2$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Missouri State University

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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Find the equations of the …

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Finding an Equation of a L…

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okay for this problem, We're going to be referencing exercise number 57 from earlier in this problem set. If you go back and look at 57 we were given two points the 20.1 half 16 and the 160.1 half negative. 73. In that problem, we found the slope of the line that connects those points. What we found was that the slope does not exist. No slope undefined. Remember, this is not a zero slope. This is no slope. It does not exist up problem for this particular problem. We want to find the equation for this line. And then we went to graft. Now we have a small problem. Most of the ways that we write equations for lines require slope. We have slope intercept. Why equals M X plus B? We have the point slope form. Why? Minus y one equals m times X minus X one. In both cases, we require the slope. But we have no slope here. It's undefined. So what does that mean? Well, slope is rise over, run in orderto have no slope. It means my run was zero is dividing by zero. That's how I haven't undefined slope, so I have no run. I'm not moving side to side at all. All my motion is up and down. So that means that this is a vertical line and vertical lines take the form of X equals some constant. If you go back and look at the original points, you'll notice that they have the same X coordinate. X equals one half. So for this line, I could let the Y value be anything I want. 16 Negative. 73 0 1,000,027 00.2 It doesn't matter what the Y value is. The X value will always have to be one half. So when I go to graph that, I'll find X equals one half on my grid, and I'm gonna do my best to make this a nice straight line. It's a little bit easier if you have a ruler, but it's going to stay right there and ex equaling a half. That's the graph of the line X equals one half

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