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(a) Find an equation for the horizontal line passing through the $y$ -intercept of the line in $41(\text { a). }(b)$ Find an equation for the vertical line passing through the $x$ -intercept of the line in $41(b).$

(a) $y=-6 / 5$(b) $x=-37/2$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Campbell University

Harvey Mudd College

Baylor 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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Yeah. This problem is referencing the lines that were found in exercise number 41 A and B. So, for your reference, I have included the final steps of both parts A and B from 41. You could see these are the two equations were referencing. If you're not sure where these came from, you can pause this video. Look back and exercise 41. You could make sure you understand where these came from. Then we'll come back, Um, and find this particular exercises goal. Okay, so let's start with part A, For part A, We're going to reference 41 a. That equation. What we want to do is find the equation for the horizontal line horizontal line that goes through the Y intercept. Okay, so what is the Y intercept? That's our first question. Well, slope intercept form puts the constant. That constant is the Y coordinate of the Y intercept. So our Y intercept is going to be zero negative. 6/5. So okay. Now. Ah, horizontal line. Ah, horizontal line has no rise. I can run as much as I want, but there's no rise. So when I look at rise overrun, I have a denominator. I could go sideways, but my rises zero, that means my slope is zero. So if I want to write this, if I want to put this into slope intercept form, why equals M X plus B? My slope is going to be zero right now. It is still going to go through that same y intercept that that hasn't changed because, you know, it has to go through that point. But the slope is zero. So I would write this as Why equals negative 6/5. Anytime you have a horizontal line, there's not going to be an ex term. It's just gonna be why equaling a constant. So in this case, that why coordinate eyes negative 6/5? So that's the constant in my equation. Okay, let's go on to part B. So I'm looking at a new equation. Y equals 2/5 X plus 37 5th. So for this problem now, I want to find a vertical line that goes through the X intercept of the given line that we have here. So how do I find the X intercept? It's not quite a straightforward just pulling off the constant, like the Y intercept the X intercept means that my why value is zero. So if I go to this equation, I put in a zero. Now I can solve for X so I can put the X by itself on one side so I can have negative to fifth X equals 37 5th. So and I'm gonna multiply both sides by negative five halves. When I do that, I just have an X on the left hand side on the right hand side. Those fives cancel. So I end up with negative 37 halfs. So that's why X intercept. It's the point. Negative. 37 halves. Zero. Okay, So horizontal meant I had all run, but no rise. A vertical line. If I look at that slope, I have all rise but no run. I'm not going anywhere sideways. So when I go to make that slope, fraction my run, my denominator is zero. That means I haven't undefined slope, so I'm not gonna put this into slope intercept form. Instead, I'm going to write this as X equals negative 37 halfs. Horizontal lines are Why equals a constant vertical lines are X equals a constant. In this case, X equals negative 37 halves

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