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(a) Find an equation for the horizontal line passing through the $y$ -intercept of the line in $42(a) .$ (b) Find an equation for the vertical line passing through the $x$ -intercept of the line in $42(b).$

(a) $y=-6$(b) $x=-14/3$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

McMaster University

Baylor 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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this problem references the solutions to the exercise. Found a few exercises back number 42 2 different equations that we're gonna be examining here. So I've copied these equations directly from exercise 42. If you're not sure where they came from, you can pause this video, go back and look at exercise 42. Then come back and rejoin us. Okay, First, let's look at the equation from 42 point a. Our first task we want to find Ah, horizontal line that passes through the Y intercept of this line. Okay, well, what is the Y? Intercept? We have been given this equation in slope intercept form, which means that that constant, including the sign, is the Y coordinate of the Y intercept. So our Y intercept zero negative six. Right. So what about horizontal? Well, horizontal lines are they go from side to side. If I look at the slope of a horizontal line, rise over run, I have no rise. But I can run a Sfar as I want to go side to side forever. I'm just never going to rise. That means I'm gonna have a numerator of zero. So my slope is going to equal zero. So if I go to put this in slope intercept form, I'm gonna have no slope. Zero slope, plus, um, plus m x plus B. So what's that? Why intercept? Well, I'm going through this y intercept right here, which means it's gonna be minus six. So my equation is Why equals negative six. Every horizontal line is going to be. Why equals a constant. So in this case, why equals negative six? Now, let's look at the second piece. Let's look at the other equation. Y equals negative. 37 X minus two. For this problem, we want to find a vertical line that goes through the X intercept. Well, finding the X intercept isn't quite as easy as the Y intercept the Y intercept. I could just literally pull the number right out of the equation. I have to do a little bit of work for the X intercept. An ex intercept has a y value of zero, so I could plug in zero for why? And then that gives me an equation. Aiken solve for X, so I could add to to both sides. And then I'm gonna multiply both sides by negative seven thirds. Okay, so those numbers cancel on the right on the left, though. Nothing canceled. So I end up with negative 14 3rd. So that's my ex intercept. Negative. 14 3rd. Zero. Okay, so there's my point. What does it mean to have a vertical line? Well, that's straight up and down. Now. If I examined that line for rise over run, I have a problem. I can rise as much as I want, but I'm not running. I'm not going side to side. It all means I'm dividing by zero. This is an undefined slope, so I'm not gonna be able to write it in our traditional slope intercept form. What I have for a vertical line is X equals a constant. So in this case, X equals negative 14 3rd. So horizontal lines have Why equals a constant vertical lines are X equals a constant

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